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Example Questions
Example Question #121 : Solving Rational Expressions
Solve for
.
To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.
Cross multiply.
Remember we are multiplying
with the expression. Now distribute.
Add
on both sides.
Divide
on both sides.
Example Question #32 : Solving Rational Expressions
Solve for
.
To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.
Cross multiply.
Remember we are multiplying
to the expression. Now distribute.
Add
on both sides.
Divide
on both sides.
Example Question #131 : Solving Rational Expressions
Solve for
.
To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.
Cross multiply.
Remember to multiply
to each of the expressions respectively. Then distribute.
Subtract
and on both sides.
Example Question #171 : Rational Expressions
Solve for
.
To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.
Cross multiply.
Remember we are multiplying
to the expressions respectively. Then distribute.
Subtract
and on both sides.
Example Question #172 : Rational Expressions
Solve for
.
To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.
Cross multiply.
Remember we are multiplying
to the expression. Then we distribute.
Subtract
on both sides.
Divide
on both sides.
Example Question #173 : Rational Expressions
Solve for
.
To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.
Distribute. Remember to apply FOIL.
Subtract
, , and on both sides.
Divide
on both sides.
Example Question #174 : Rational Expressions
Simplify:
To simplify the expressions, we will need a least common denominator.
Multiply the two denominators together to obtain the least common denominator.
Convert the fractions.
Combine the fractions as one fraction.
Simplify the numerator and combine like-terms.
The answer is:
Example Question #691 : Intermediate Single Variable Algebra
When considering the solution space for a rational function, we must look at the denominator.
Any value of x in the denominator that results in a zero cannot be part of the solution space because it is a mathematical impossibility to divide by 0.
(add 16 to both sides)
(take the square root of both sides)
If we were to plug in a positive or negative 4 into the function, both of these would result in a zero in the denominator, which is a mathematical impossibility.
Example Question #173 : Rational Expressions
Solve:
Convert the fractions to a common denominator.
Simplify the top and bottom and combine like terms on the numerator.
The answer is:
Example Question #1831 : Algebra Ii
Solve:
Find the least common denominator by multiplying both denominators together.
Convert the fractions.
Simplify the numerator and denominator.
Combine both fractions together. Remember to brace the second numerator in parentheses.
Simplify the fraction.
Factor out a negative one in the denominator.
The answer is:
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