GRE Quantitative Reasoning - How to evaluate rational expressions

Function_part1

9/5

–37/15

–11/5

37/15

–9/5

Explanation

Fraction_part2

Fraction_part3

Evaluate the following rational expression, if :

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

$\frac{11}{2}$

$\frac{9}{2}$

$\frac{10}{2}$

$\frac{16}{2}$

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.

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

$=\frac{11}{2}$

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

$-\frac{6}{5}$

$-\frac{3}{6}$

$-\frac{6}{7}$

$\frac{6}{5}$

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.

$-\frac{6}{5}$

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

$\frac{4}{5}$

$-\frac{4}{5}$

$\frac{5}{4}$

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.

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

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

$\frac{2}{3}$

$\frac{3}{2}$

$-\frac{4}{6}$

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

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:

$\frac{2}{3}$

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

$\frac{33}{5}$

$\frac{32}{5}$

$\frac{23}{5}$

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.

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

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

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.

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

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

$-\frac{5}{3}$

$\frac{5}{3}$

$\frac{10}{3}$

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.

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

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

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.

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

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

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.

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

How to evaluate rational expressions

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