Question 1

Add the following rational expressions and simplify: $$\frac{3}{8} + \frac{7}{8}$$

Accepted Answer

$$\frac{5}{4}$$

Question 2

Add the following rational expressions and simplify: $$\frac{4}{3} + \frac{1}{3}$$

Accepted Answer

$$\frac{5}{3}$$

Question 3

Add the following rational expressions and simplify: $$\frac{9}{5} + \frac{14}{7}$$

Accepted Answer

$$\frac{133}{35}$$

Question 4

Subtract and simplify: $$\frac{z^2$}{z+7} - \frac{49}{z+7}$$

Accepted Answer

$$\frac{z^2$ - 49}{z+7}$$

Question 5

Find the sum and simplify: $$\frac{1}{7w} + \frac{8}{5w}$$

Accepted Answer

$$\frac{13}{35w}$$

Question 6

Subtract and simplify: $$\frac{y+8}{y^2$-4y+3} - \frac{2}{y^2$-1}$$

Accepted Answer

$$\frac{(y+8)(y^2$-1) - 2(y^2$-4y+3)}{(y^2$-4y+3)(y^2-1$$)}$

Question 7

Which of the following is the least common denominator (LCD) for $$\frac{1}{x^2$-4}$$ and $$\frac{1}{x+2}$$?

Accepted Answer

$$x^2-4$

Question 8

Find the LCD for the rational expressions $$\frac{1}{x^2$-9}$$ and $$\frac{1}{x-3}.$$

Accepted Answer

$$x^2-9$

Question 9

A chemist is mixing two solutions. The first solution is $$\frac{2}{x}$$ liters and the second is $$\frac{3}{x}$$ liters. What is the total volume?

Accepted Answer

$$\frac{5}{x}$$ liters

Question 10

A medical researcher subtracts the error rates of two tests: $$\frac{5}{n}$$ and $$\frac{2}{n}. $$What is the difference?

Accepted Answer

$$\frac{3}{n}$$

Question 11

Add and simplify: $$\frac{2}{x+1} + \frac{3}{x+1}$$

Accepted Answer

$$\frac{5}{x+1}$$

Question 12

Subtract and simplify: $$\frac{5x}{x^2$-1} - \frac{2}{x-1}$$

Accepted Answer

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

Question 13

Which of the following is the LCD for $$\frac{1}{x^2$-4x+4}$$ and $$\frac{1}{x-2}$$?

Accepted Answer

$$(x-2)^2$$

Question 14

A company’s profit per unit is modeled by $$\frac{10}{x}$$ and its cost per unit by $$\frac{4}{x}. $$What is the profit minus cost per unit?

Accepted Answer

$$\frac{6}{x}$$

Question 15

Add and simplify: $$\frac{2}{x} + \frac{3}{x^2$}$$

Accepted Answer

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

Question 16

Subtract and simplify: $$\frac{4}{x+2} - \frac{1}{x+2}$$

Accepted Answer

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

Question 17

A biologist measures the growth rates of two bacteria cultures: $$\frac{7}{t}$$ and $$\frac{3}{t}. $$What is the combined growth rate?

Accepted Answer

$$\frac{10}{t}$$

Question 18

Find the LCD for $$\frac{1}{x^2$-1}$$ and $$\frac{1}{x+1}.$$

Accepted Answer

$$x^2-1$

Question 19

Subtract and simplify: $$\frac{5}{x-3} - \frac{2}{x-3}$$

Accepted Answer

$$\frac{3}{x-3}$$

Intermediate Algebra Study Guide: Adding, Subtracting, and Finding LCD of Rational Expressions

Study Guide - Practice Questions