How to divide rational expressions - PSAT Math
Card 0 of 7
Which of the following is equivalent to 
? Assume that denominators are always nonzero.
Which of the following is equivalent to
We will need to simplify the expression 
. We can think of this as a large fraction with a numerator of 
and a denominator of 
.
In order to simplify the numerator, we will need to combine the two fractions. When adding or subtracting fractions, we must have a common denominator. 
has a denominator of 
, and 
has a denominator of 
. The least common denominator that these two fractions have in common is 
. Thus, we are going to write equivalent fractions with denominators of 
.
In order to convert the fraction 
to a denominator with 
, we will need to multiply the top and bottom by 
.
Similarly, we will multiply the top and bottom of 
by 
.
We can now rewrite 
as follows:
= 
Let's go back to the original fraction 
. We will now rewrite the numerator:
= 
To simplify this further, we can think of 
as the same as 
. When we divide a fraction by another quantity, this is the same as multiplying the fraction by the reciprocal of that quantity. In other words, 
.
= 
Lastly, we will use the property of exponents which states that, in general, 
.
The answer is 
.
We will need to simplify the expression
In order to simplify the numerator, we will need to combine the two fractions. When adding or subtracting fractions, we must have a common denominator.
In order to convert the fraction
Similarly, we will multiply the top and bottom of
We can now rewrite
Let's go back to the original fraction
To simplify this further, we can think of
Lastly, we will use the property of exponents which states that, in general,
The answer is
Compare your answer with the correct one above
Which of the following is equivalent to ? Assume that denominators are always nonzero.
Which of the following is equivalent to
We will need to simplify the expression . We can think of this as a large fraction with a numerator of and a denominator of .
In order to simplify the numerator, we will need to combine the two fractions. When adding or subtracting fractions, we must have a common denominator. has a denominator of , and has a denominator of . The least common denominator that these two fractions have in common is . Thus, we are going to write equivalent fractions with denominators of .
In order to convert the fraction to a denominator with , we will need to multiply the top and bottom by .
Similarly, we will multiply the top and bottom of by .
We can now rewrite as follows:
=
Let's go back to the original fraction . We will now rewrite the numerator:
=
To simplify this further, we can think of as the same as . When we divide a fraction by another quantity, this is the same as multiplying the fraction by the reciprocal of that quantity. In other words, .
=
Lastly, we will use the property of exponents which states that, in general, .
The answer is .
We will need to simplify the expression
In order to simplify the numerator, we will need to combine the two fractions. When adding or subtracting fractions, we must have a common denominator.
In order to convert the fraction
Similarly, we will multiply the top and bottom of
We can now rewrite
Let's go back to the original fraction
To simplify this further, we can think of
Lastly, we will use the property of exponents which states that, in general,
The answer is
Compare your answer with the correct one above
Which of the following is equivalent to ? Assume that denominators are always nonzero.
Which of the following is equivalent to
We will need to simplify the expression . We can think of this as a large fraction with a numerator of and a denominator of .
In order to simplify the numerator, we will need to combine the two fractions. When adding or subtracting fractions, we must have a common denominator. has a denominator of , and has a denominator of . The least common denominator that these two fractions have in common is . Thus, we are going to write equivalent fractions with denominators of .
In order to convert the fraction to a denominator with , we will need to multiply the top and bottom by .
Similarly, we will multiply the top and bottom of by .
We can now rewrite as follows:
=
Let's go back to the original fraction . We will now rewrite the numerator:
=
To simplify this further, we can think of as the same as . When we divide a fraction by another quantity, this is the same as multiplying the fraction by the reciprocal of that quantity. In other words, .
=
Lastly, we will use the property of exponents which states that, in general, .
The answer is .
We will need to simplify the expression
In order to simplify the numerator, we will need to combine the two fractions. When adding or subtracting fractions, we must have a common denominator.
In order to convert the fraction
Similarly, we will multiply the top and bottom of
We can now rewrite
Let's go back to the original fraction
To simplify this further, we can think of
Lastly, we will use the property of exponents which states that, in general,
The answer is
Compare your answer with the correct one above
Which of the following is equivalent to ? Assume that denominators are always nonzero.
Which of the following is equivalent to
We will need to simplify the expression . We can think of this as a large fraction with a numerator of and a denominator of .
In order to simplify the numerator, we will need to combine the two fractions. When adding or subtracting fractions, we must have a common denominator. has a denominator of , and has a denominator of . The least common denominator that these two fractions have in common is . Thus, we are going to write equivalent fractions with denominators of .
In order to convert the fraction to a denominator with , we will need to multiply the top and bottom by .
Similarly, we will multiply the top and bottom of by .
We can now rewrite as follows:
=
Let's go back to the original fraction . We will now rewrite the numerator:
=
To simplify this further, we can think of as the same as . When we divide a fraction by another quantity, this is the same as multiplying the fraction by the reciprocal of that quantity. In other words, .
=
Lastly, we will use the property of exponents which states that, in general, .
The answer is .
We will need to simplify the expression
In order to simplify the numerator, we will need to combine the two fractions. When adding or subtracting fractions, we must have a common denominator.
In order to convert the fraction
Similarly, we will multiply the top and bottom of
We can now rewrite
Let's go back to the original fraction
To simplify this further, we can think of
Lastly, we will use the property of exponents which states that, in general,
The answer is
Compare your answer with the correct one above
Which of the following is equivalent to ? Assume that denominators are always nonzero.
Which of the following is equivalent to
We will need to simplify the expression . We can think of this as a large fraction with a numerator of and a denominator of .
In order to simplify the numerator, we will need to combine the two fractions. When adding or subtracting fractions, we must have a common denominator. has a denominator of , and has a denominator of . The least common denominator that these two fractions have in common is . Thus, we are going to write equivalent fractions with denominators of .
In order to convert the fraction to a denominator with , we will need to multiply the top and bottom by .
Similarly, we will multiply the top and bottom of by .
We can now rewrite as follows:
=
Let's go back to the original fraction . We will now rewrite the numerator:
=
To simplify this further, we can think of as the same as . When we divide a fraction by another quantity, this is the same as multiplying the fraction by the reciprocal of that quantity. In other words, .
=
Lastly, we will use the property of exponents which states that, in general, .
The answer is .
We will need to simplify the expression
In order to simplify the numerator, we will need to combine the two fractions. When adding or subtracting fractions, we must have a common denominator.
In order to convert the fraction
Similarly, we will multiply the top and bottom of
We can now rewrite
Let's go back to the original fraction
To simplify this further, we can think of
Lastly, we will use the property of exponents which states that, in general,
The answer is
Compare your answer with the correct one above
Which of the following is equivalent to ? Assume that denominators are always nonzero.
Which of the following is equivalent to
We will need to simplify the expression . We can think of this as a large fraction with a numerator of and a denominator of .
In order to simplify the numerator, we will need to combine the two fractions. When adding or subtracting fractions, we must have a common denominator. has a denominator of , and has a denominator of . The least common denominator that these two fractions have in common is . Thus, we are going to write equivalent fractions with denominators of .
In order to convert the fraction to a denominator with , we will need to multiply the top and bottom by .
Similarly, we will multiply the top and bottom of by .
We can now rewrite as follows:
=
Let's go back to the original fraction . We will now rewrite the numerator:
=
To simplify this further, we can think of as the same as . When we divide a fraction by another quantity, this is the same as multiplying the fraction by the reciprocal of that quantity. In other words, .
=
Lastly, we will use the property of exponents which states that, in general, .
The answer is .
We will need to simplify the expression
In order to simplify the numerator, we will need to combine the two fractions. When adding or subtracting fractions, we must have a common denominator.
In order to convert the fraction
Similarly, we will multiply the top and bottom of
We can now rewrite
Let's go back to the original fraction
To simplify this further, we can think of
Lastly, we will use the property of exponents which states that, in general,
The answer is
Compare your answer with the correct one above
Which of the following is equivalent to ? Assume that denominators are always nonzero.
Which of the following is equivalent to
We will need to simplify the expression . We can think of this as a large fraction with a numerator of and a denominator of .
In order to simplify the numerator, we will need to combine the two fractions. When adding or subtracting fractions, we must have a common denominator. has a denominator of , and has a denominator of . The least common denominator that these two fractions have in common is . Thus, we are going to write equivalent fractions with denominators of .
In order to convert the fraction to a denominator with , we will need to multiply the top and bottom by .
Similarly, we will multiply the top and bottom of by .
We can now rewrite as follows:
=
Let's go back to the original fraction . We will now rewrite the numerator:
=
To simplify this further, we can think of as the same as . When we divide a fraction by another quantity, this is the same as multiplying the fraction by the reciprocal of that quantity. In other words, .
=
Lastly, we will use the property of exponents which states that, in general, .
The answer is .
We will need to simplify the expression
In order to simplify the numerator, we will need to combine the two fractions. When adding or subtracting fractions, we must have a common denominator.
In order to convert the fraction
Similarly, we will multiply the top and bottom of
We can now rewrite
Let's go back to the original fraction
To simplify this further, we can think of
Lastly, we will use the property of exponents which states that, in general,
The answer is
Compare your answer with the correct one above