Expressions - GRE Quantitative Reasoning

Since both expressions have a common denominator, x2, we can just recopy the denominator and focus on the numerators. We get (9x - 2) - (6x - 8). We must distribute the negative sign over the 6x - 8 expression which gives us 9x - 2 - 6x + 8 ( -2 minus a -8 gives a +6 since a negative and negative make a positive). The numerator is therefore 3x + 6.

Factor first. The numerators will not factor, but the first denominator factors to (x – 2)(x + 2) and the second denomintaor factors to x(x – 2). Multiplying fractions does not require common denominators, so now look for common factors to divide out. There is a factor of x and a factor of (x + 2) that both divide out, leaving 4 in the numerator and two factors of (x – 2) in the denominator.

Substitute the values into equation: 3(-4) - 5(7) = -12 - 35 = -47.

The answer is 2.

First solve for the constant x:

3_x_ + 2 = 32

x = 10

Now plug in x = 10 and b = 12:

a(10) + 12 = 32

a = 2

Since both expressions have a common denominator, x2, we can just recopy the denominator and focus on the numerators. We get (9x - 2) - (6x - 8). We must distribute the negative sign over the 6x - 8 expression which gives us 9x - 2 - 6x + 8 ( -2 minus a -8 gives a +6 since a negative and negative make a positive). The numerator is therefore 3x + 6.

Factor first. The numerators will not factor, but the first denominator factors to (x – 2)(x + 2) and the second denomintaor factors to x(x – 2). Multiplying fractions does not require common denominators, so now look for common factors to divide out. There is a factor of x and a factor of (x + 2) that both divide out, leaving 4 in the numerator and two factors of (x – 2) in the denominator.

Substitute the values into equation: 3(-4) - 5(7) = -12 - 35 = -47.

The answer is 2.

First solve for the constant x:

3_x_ + 2 = 32

x = 10

Now plug in x = 10 and b = 12:

a(10) + 12 = 32

a = 2

Since both expressions have a common denominator, x2, we can just recopy the denominator and focus on the numerators. We get (9x - 2) - (6x - 8). We must distribute the negative sign over the 6x - 8 expression which gives us 9x - 2 - 6x + 8 ( -2 minus a -8 gives a +6 since a negative and negative make a positive). The numerator is therefore 3x + 6.

Factor first. The numerators will not factor, but the first denominator factors to (x – 2)(x + 2) and the second denomintaor factors to x(x – 2). Multiplying fractions does not require common denominators, so now look for common factors to divide out. There is a factor of x and a factor of (x + 2) that both divide out, leaving 4 in the numerator and two factors of (x – 2) in the denominator.

Substitute the values into equation: 3(-4) - 5(7) = -12 - 35 = -47.

The answer is 2.

First solve for the constant x:

3_x_ + 2 = 32

x = 10

Now plug in x = 10 and b = 12:

a(10) + 12 = 32

a = 2

Since both fractions in the expression have a common denominator of , we can combine like terms into a single numerator over the denominator:

Since both rational terms in the expression have the common denominator , combine the numerators and simplify like terms:

Since both terms in the expression have the common denominator , combine the fractions and simplify the numerators:

When adding rational expressions with common denominators, you simply need to add the like terms in the numerator.

Therefore, is the best answer.

Since both fractions in the expression have a common denominator of , we can combine like terms into a single numerator over the denominator: