Question 1

Subtract and simplify the following rational expressions:

$$\displaystyle \frac{-5a}{a^2$ - a - 2} - \frac{10}{a^2$ - a - 2}$$

Accepted Answer

$$\displaystyle \frac{-5a - 10}{a^2$ - a - 2}$$

Question 2

Add and simplify the following rational expressions:

$$\displaystyle \frac{y+8}{y-2} + \frac{y+9}{y-2}$$

Accepted Answer

$$\displaystyle \frac{2y+17}{y-2}$$

Question 3

Subtract and simplify:

$$\displaystyle \frac{-6x^2$}{x+4} - \frac{16+5x^2$}{x+4}$$

Accepted Answer

$$\displaystyle \frac{-6x^2$ - 16 - 5x^2$}{x+4}$$

Question 4

Find the least common denominator (LCD) for the following rational expressions:

$$\displaystyle \frac{1}{10x}, \quad \frac{5}{2x+2}$$

Accepted Answer

$$\displaystyle 10x(x+1)$$

Question 5

Find the LCD for the following rational expressions:

$$\displaystyle \frac{2}{x+2}, \quad \frac{9}{x-4}$$

Accepted Answer

$$\displaystyle (x+2)(x-4)$$

Question 6

Find the LCD for the following rational expressions:

$$\displaystyle \frac{19}{4x+8}, \quad \frac{15}{2x^2$+8x+8}$$

Accepted Answer

$$\displaystyle 4(x+2)(x+1)$$

Question 7

Rewrite the rational expression $$\displaystyle \frac{5}{8x+24}$$ with the denominator $$8z(x+3).$$

Accepted Answer

$$\displaystyle \frac{5z}{8z(x+3)}$$

Question 8

Rewrite the rational expression $$\displaystyle \frac{7t+9}{15t+24}$$ with the denominator $$3s(5t+8).$$

Accepted Answer

$$\displaystyle \frac{(7t+9)3s}{3s(5t+8)}$$

Question 9

Rewrite the rational expression $$\displaystyle \frac{x}{x^3$+7x^2+6x$$}$$ with the denominator x(x+7)(x+1)(x+6$$)$.

Accepted Answer

$$\displaystyle \frac{x}{x(x+7)(x+1)(x+6)}$$

Question 10

Perform the indicated operation and simplify:

$$\displaystyle \frac{49}{7x} + \frac{36}{6x}$$

Accepted Answer

$$\displaystyle \frac{49 \cdot 6 + 36 \cdot 7}{42x}$$

Question 11