Question 1

Which of the following is the correct result of adding the rational expressions $$\frac{x+3}{x+6} + \frac{x-4}{x+6}$$?

Accepted Answer

Question 2

What is the least common denominator (LCD) of the rational expressions $$\frac{1}{18x^3$y}$$ and $$\frac{5}{27x^2$y^3$$}$?

Accepted Answer

$$54x^3y^3$

Question 3

Which of the following is the correct result of $$\frac{a}{a-6} - \frac{3a-12}{a-6}$$?

Accepted Answer

$$\frac{-2a+12}{a-6}$$

Question 4

Find the LCD for the following rational expressions: $$\frac{7}{x^2$(x+1)}$$ and $$\frac{3z}{x(x+1)^3$}.$$

Accepted Answer

$$x^2(x+1)^3$

Question 5

Which of the following is the correct result of $$\frac{2}{x^2$y} + \frac{5}{3x^3$y}$$?

Accepted Answer

Question 6

A chemist is mixing two solutions. The first solution is represented by $$\frac{4x}{x^2$-x-12}$$ and the second by $$\frac{6x^2$}{x^2$-7x+12}. $$What is the LCD of these two rational expressions?

Accepted Answer

Question 7

Which of the following is the correct result of $$\frac{2x-6}{x-1} - \frac{4}{1-x}$$?

Accepted Answer

$$\frac{2x-2}{x-1}$$

Question 8

A medical researcher is analyzing the sum $$\frac{5x+2}{x^2$+2x-8} + \frac{2-4x}{x^2$+2x-8}. $$What is the simplified result?

Accepted Answer

$$\frac{x+4}{x^2$+2x-8}$$

Question 9

Which of the following is the correct result of $$\frac{2x}{x^2$-9} - \frac{3}{x^2$-4x+3}$$?

Accepted Answer

$$\frac{2x(x-1)-3(x+3)}{(x-3)(x+3)(x-1)}$$

Question 10

A pharmacist needs to combine two medications represented by $$\frac{3}{x+3}$$ and $$\frac{5}{x^2$+6x+9} - \frac{x}{x^2$-9}. $$What is the LCD for these three rational expressions?

Accepted Answer

$$(x+3)^2(x-3$$)$$

Question 11

Which of the following is the correct result of $$\frac{3+2y}{y^2$-1} - \frac{y+3}{y^2$-1}$$?

Accepted Answer

$$\frac{y+6}{y^2$-1}$$

Question 12

A biologist is working with the sum $$\frac{2x}{3x^2$-13x+4} + \frac{5}{x^2$-2x-8}. $$What is the LCD of these two rational expressions?

Accepted Answer

$$(3x+1)(x-4)(x+2)$$

Question 13

Which of the following is the correct result of $$\frac{10}{3x-3} + \frac{1}{7x-7}$$?

Accepted Answer

$$\frac{10(7x-7)+1(3x-3)}{(3x-3)(7x-7)}$$

Question 14

A student is asked to simplify $$\frac{-2}{x^2$-3x} - \frac{1}{x^3$-3x^2$$}$. What is the LCD of these two rational expressions?

Accepted Answer

$$x^3-3x^2$

Question 15

Which of the following is the correct result of $$\frac{2}{x-2} + \frac{x}{x-2}$$?

Accepted Answer

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

Question 16

A civil engineer is working with the sum $$\frac{4}{x^2$y-2} + \frac{x}{x^2$y}. $$What is the LCD of these two rational expressions?

Accepted Answer

$$x^2y(x^2$y-2)$

Question 17

Which of the following is the correct result of $$\frac{5}{3x-6} - \frac{x}{x-2} + 3 + \frac{2x}{5x-10}$$?

Accepted Answer

Adding and Subtracting Rational Expressions in Intermediate Algebra

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