GRE Math : How to evaluate rational expressions

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Example Questions

Example Question #11 : How To Evaluate Rational Expressions

Evaluate $\frac{z^2 + 2z - 20}{3}$ if z = 3 .

Possible Answers:

$\frac{5}{3}$

$\frac{10}{3}$

$-\frac{5}{3}$

Correct answer:

$-\frac{5}{3}$

Explanation:

To evaluate, simply plug in for :

$\frac{z^2 + 2z - 20}{3}$

$\frac{3^2 + (2\cdot 3)-20}{3}$

Remembering the order of operations we are able to solve this problem. The order of operations is parentheses, exponents, multiplication, division, addition, subtraction.

$\frac{9 + (6)-20}{3}=\frac{15-20}{3}=-\frac{5}{3}$

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Example Question #12 : How To Evaluate Rational Expressions

Evaluate $\frac{x^3 + x^2}{x}$ if x = 2 .

Possible Answers:

Correct answer:

Explanation:

To evaluate, simply plug in for :

$\frac{x^3 + x^2}{x}$

$\frac{2^3 + 2^2}{2}$

Recall that we must simplify the exponents before we are able to add the numerator and divide by the denominator.

$\frac{8 + 4}{2}=\frac{12}{2}$

From here we can reduce the fraction by factoring out a two from both the numerator and the denominator.

$\frac{12}{2}=\frac{2\cdot 6}{2\cdot 1}=\frac{6}{1}=6$

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Example Question #13 : How To Evaluate Rational Expressions

Evaluate $\frac{3x^2 + 9x -18}{2x^2 + x}$ if x = -1 .

Possible Answers:

Correct answer:

Explanation:

To solve, simply plug in for :

$\frac{3x^2 + 9x -18}{2x^2 + x}$

$\frac{3(-1)^2 + 9(-1) -18}{2(-1)^2 + -1}$

According to the order of operations we must simplify the exponents first. Then we will multiply the necessary terms and finally we will add and subtract the terms as specified.

$=\frac{3(1)-9-18}{2(1)-1}=\frac{3 -27}{2-1}$

$=\frac{-24}{1}=-24$

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Example Question #31 : Rational Expressions

Evaluate $\frac{7y^2 - 8y}{y + 12}$ if y = 4 .

Possible Answers:

Correct answer:

Explanation:

To solve, simply plug in for :

$\frac{7y^2 - 8y}{y + 12}$

$\frac{7(4^2) - 8(4)}{4 + 12}$

First we must simplify the exponents. The we will multiply each of the two terms in the numerator. After that, we can add the terms in denominator and subtract the terms in the numerator.

$\frac{7(16)-32}{16}=\frac{112-32}{16}$

Sutracting the terms on top gives:

$\frac{80}{16}$ .

We can simplify this fraction by factoring out a sixteen from both the numerator and denominator.

$\frac{80}{16}=\frac{16\cdot 5}{16 \cdot 1}=\frac{5}{1}=5$

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GRE Math : How to evaluate rational expressions

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #11 : How To Evaluate Rational Expressions

Example Question #12 : How To Evaluate Rational Expressions

Example Question #13 : How To Evaluate Rational Expressions

Example Question #31 : Rational Expressions

All GRE Math Resources

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