GRE Math : Rational Expressions

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Example Question #1 : How To Evaluate Rational Expressions

Evaluate the following rational expression, if x = 2 :

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

Possible Answers:

$\frac{9}{2}$

$\frac{16}{2}$

$\frac{10}{2}$

$\frac{11}{2}$

Correct answer:

$\frac{11}{2}$

Explanation:

To evaluate, simply plug in the number for :

$\frac{2(2^2) + 3}{2}=$

Remembering to use order of operations (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) we arrive at our final solution.

$\frac{2(4)+3}{2}=\frac{8+3}{2}$

$=\frac{11}{2}$

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Example Question #2 : How To Evaluate Rational Expressions

If y = 3 , find $\frac{2y}{y -8}$ .

Possible Answers:

$-\frac{6}{7}$

$-\frac{3}{6}$

$-\frac{6}{5}$

$\frac{6}{5}$

Correct answer:

$-\frac{6}{5}$

Explanation:

To solve, simply plug in for :

$\frac{2y}{y -8}=$

Remembering to use the correct order of operations (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) we arrive at our final answer.

First do the multiplication that is in the numerator.

$\frac{2(3)}{3-8}=$

Now do the subtraction in the denominator.

$-\frac{6}{5}$

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Example Question #3 : How To Evaluate Rational Expressions

Find $\frac{2x^2 - 2x}{5}$ if x = -1 .

Possible Answers:

$-\frac{4}{5}$

$\frac{5}{4}$

$\frac{4}{5}$

Correct answer:

$\frac{4}{5}$

Explanation:

To solve, simply plug in for :

$\frac{2x^2 - 2x}{5} =$

Remembering to use the correct order of operations (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) we arrive at the final solution.

$\frac{2(-1^2) - 2(-1))}{5} =$

Also recall that when a negative number is squared it becomes a positive number. This is also true when we multiply two negative numbers together.

$\frac{2(1)+1}{5}=$ $\frac{4}{5}$

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Example Question #4 : How To Evaluate Rational Expressions

Evaluate $\frac{x^2 - 3x}{x + 2}$ if x = 4 .

Possible Answers:

$\frac{3}{2}$

$-\frac{2}{3\frac{}{}}$

$-\frac{4}{6}$

$\frac{2}{3}$

Correct answer:

$\frac{2}{3}$

Explanation:

To evaluate, merely plug in for :

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

$\frac{4^2 - (3\cdot4)}{4 + 2} =$

Remembering order of operations (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) we arrive at our final solution.

$\frac{16-(12)}{6}=\frac{4}{6}$

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

$\frac{4}{6} =\frac{2\cdot 2}{2\cdot 3}$

Canceling out the two's we get:

$\frac{2}{3}$

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Example Question #5 : How To Evaluate Rational Expressions

Evaluate $\frac{y^3 - 3}{y - 3}$ if y = 0 .

Possible Answers:

Correct answer:

Explanation:

To solve, simply plug in for :

$\frac{y^3 - 3}{y - 3}$

$\frac{0^3 - 3}{0 - 3}$

Recall that when a negative number is divided by another negative number it results in a positive number.

$\frac{-3}{-3}=1$

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Example Question #6 : How To Evaluate Rational Expressions

Evaluate $\frac{x^2 + 2x - 2}{x}$ if x = 5 .

Possible Answers:

$\frac{23}{5}$

$\frac{33}{5}$

$\frac{32}{5}$

Correct answer:

$\frac{33}{5}$

Explanation:

To evaluate, simply plug in for :

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

$\frac{5^2 + 2(5) - 2}{5} =$

Remembering the order of operations (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) we arrive at our final solution.

$=\frac{25+10-2}{5}=\frac{35-2}{5}=\frac{33}{5}$

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Example Question #7 : How To Evaluate Rational Expressions

Evaluate $\frac{5n^2}{-2n - 8}$ if n = -2 .

Possible Answers:

Correct answer:

Explanation:

To solve, simply plug in for :

$\frac{5n^2}{-2n - 8}$

$\frac{5(-2)^2}{(-2\cdot-2)-8}$

Remembering the order of operations (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) we arrive at our final solution. Also recall that multiplying two negative numbers together leads to a positive product; this is also true when you square a negative number.

$\frac{5(4)}{4-8}=\frac{20}{-4}$

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

$\frac{4\cdot 5}{4 \cdot -1}=-\frac{5}{1}=-5$

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Example Question #11 : How To Evaluate Rational Expressions

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

Possible Answers:

$\frac{10}{3}$

$\frac{5}{3}$

$-\frac{5}{3}$

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 #301 : Algebra

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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GRE Math : Rational Expressions

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 : How To Evaluate Rational Expressions

Example Question #2 : How To Evaluate Rational Expressions

Example Question #3 : How To Evaluate Rational Expressions

Example Question #4 : How To Evaluate Rational Expressions

Example Question #5 : How To Evaluate Rational Expressions

Example Question #6 : How To Evaluate Rational Expressions

Example Question #7 : How To Evaluate Rational Expressions

Example Question #11 : How To Evaluate Rational Expressions

Example Question #12 : How To Evaluate Rational Expressions

Example Question #301 : Algebra

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