Quiz about Reviewer for Final Exam

Question 1

Perform the indicated operation and simplify as much as possible.

$$\frac{x^2+5x+4}{x^2+4x+3} imes\frac{5x^2+15x}{x+4}$$

Accepted Answer

$$5x$$

Answer

$$x$$

Answer

$$3x$$

Answer

$$7x$$

Question 2

$$\frac{x^2-4}{x^2+4x+4} imes\frac{7}{x-2}$$

Accepted Answer

$$\frac{7}{x+2}$$

Answer

$$\frac{7}{x-2}$$

Answer

$$\frac{7}{x+4}$$

Answer

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

Question 3

$$\frac{4x^2-12x}{5x+10} imes\frac{x+2}{x}\div\frac{x-3}{1}$$

Accepted Answer

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

Answer

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

Answer

$$\frac{\left(x+2\right)}{5x}$$

Answer

$$\frac{x}{5\left(x+2\right)}$$

Question 4

$$\frac{4x^3-4x}{x}\div\frac{2x-2}{x-4}$$

Accepted Answer

$$2\left(x+1\right)\left(x-4\right)$$

Answer

$$\frac{x-4}{2}$$

Answer

$$\frac{\left(x-1\right)\left(x+4\right)}{2}$$

Answer

$$\frac{1}{2}$$

Question 5

$$\frac{2x^3+8x}{x+1}\div\frac{x}{2x^2-2}$$

Accepted Answer

$$4\left(x^2+4\right)\left(x-1\right)$$

Answer

$$4\left(x^2+4\right)$$

Answer

$$2\left(x+1\right)$$

Answer

$$2x\left(x^2+4\right)$$

Question 6

$$\frac{3x-1}{x^2+2x-15}-\frac{2}{x+5}$$

Accepted Answer

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

Answer

$$\frac{x-3}{x^2-2x-15}$$

Answer

$$\frac{3x-3}{x^2+2x-15}$$

Answer

$$\frac{x+5}{x-3}$$

Question 7

$$\frac{-4}{2+\frac{-4}{2+\frac{-4}{2+\frac{-4}{2+\frac{-4}{2+...}}}}}$$

Accepted Answer

$$x^2+2x+4$$

Answer

$$x^2-2x+4$$

Answer

$$x^2+2x-4$$

Answer

$$-x^2+2x-4$$

Question 8

$$\frac{2}{x+7}+\frac{1}{x-7}$$

Accepted Answer

$$\frac{3x-7}{\left(x+7\right)\left(x-7\right)}$$

Answer

$$\frac{3x-21}{\left(x+7\right)\left(x-7\right)}$$

Answer

$$\frac{x+21}{\left(x+7\right)\left(x-7\right)}$$

Answer

$$\frac{x-21}{\left(x+7\right)\left(x-7\right)}$$

Question 9

$$\frac{2}{x-6}-\frac{x-9}{x^2-3x-18}$$

Accepted Answer

$$\frac{x+15}{\left(x+3\right)\left(x-6\right)}$$

Answer

$$\frac{x+15}{\left(x+3\right)\left(x+6\right)}$$

Answer

$$\frac{x-15}{\left(x+3\right)\left(x-6\right)}$$

Answer

$$\frac{3x+15}{\left(x+3\right)\left(x-6\right)}$$

Question 10

Simplify the given rational expressions and state the excluded values:

$$\frac{4x}{8x^3+16x^2}$$

Accepted Answer

$$\frac{1}{2\left(x^2+2x\right)}$$ Excluded values: 0, -2

Answer

$$\frac{2}{\left(x^2+2x\right)}$$

Excluded values: 0, 2

Answer

$$\frac{1}{\left(2x^2+3x\right)}$$

Excluded values: 2, -2

Answer

$$\frac{1}{8x\left(x^2+2x\right)}$$

Excluded values: -2, 0

Question 11

Simplify the expression: $$\frac{x^2+4x-60}{x^2+2x-3} imes\frac{x^2+5x+6}{x^2+12x+20}$$

Accepted Answer

$$\frac{x-6}{x-1}$$

Answer

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

Answer

$$\frac{x-6}{x-3}$$

Answer

$$\frac{x+10}{x-1}$$

Question 12

Perform the indicated operation and reduce the answer to the lowest term.

$$3x^2y\ imes\ \frac{2y}{xy^2}.$$

Accepted Answer

$$6x$$

Answer

$$\frac{6}{xy}$$

Answer

$$5x$$

Answer

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

Question 13

Simplify: $$\frac{7x^2+3x-4}{x+8}\div\left(7x-4\right).$$

Accepted Answer

$$\frac{x+1}{x+8}$$

Answer

$$\frac{x-8}{x-1}$$

Answer

$$\frac{x+1}{x-8}$$

Answer

$$\frac{x-8}{x+1}$$

Question 14

Perform the indicated operation and simplify:

$$2xy\ \div\frac{2x^2}{y}$$

Accepted Answer

$$\frac{y^2}{x}$$

Answer

$$\frac{x}{y}$$

Answer

$$\frac{x^2}{y}$$

Answer

$$\frac{y^2}{x^2}$$

Question 15

Divide the following expression:

$$\frac{c-1}{c^2-c-30}\div\frac{c-5}{c^2-11c+30}$$

Accepted Answer

$$\frac{c-1}{c+5}$$

Answer

$$\frac{c+4}{c+7}$$

Answer

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

Answer

$$\frac{c-5}{c-1}$$

Question 16

Divide using synthetic division:

$$\frac{7x^2-23x+6}{x-3}.$$

Accepted Answer

$$7x-2$$

Answer

$$x^2+5x-2$$

Answer

$$7x^2-2$$

Answer

$$x^2+7x+2$$

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