Simplifying rational expressions Quiz 1

Question 1

Simplify the following expression $$\dfrac{\left( 3-x \right)}{{{x}^{2}}+3x-18}$$

Accepted Answer

$$\dfrac{-1}{x+6}$$

Answer

$$\dfrac{1}{x+6}$$

Answer

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

Answer

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

Question 2

Simplify the following expression $$\dfrac{{{x}^{3}}+216}{{{x}^{2}}-36}$$

Accepted Answer

$$x+\dfrac{36}{x-6}$$

Answer

$$\left( x-6 \right)$$

Answer

$$\left( x+6 \right)$$

Answer

$$x-\dfrac{36}{x-6}$$

Question 3

Simplify the following expression $$\dfrac{{{x}^{2}}+x-30}{3{{x}^{2}}+18x}$$

Accepted Answer

$$\dfrac{x-5}{3x}$$

Answer

$$\dfrac{x+5}{3x}$$

Answer

$$\dfrac{x+5}{3}$$

Answer

$$\dfrac{x-5}{3}$$

Question 4

Simplify the following expression $$\dfrac{xy-4x+2y-8}{{{y}^{2}}-7y+12}$$

Accepted Answer

$$\dfrac{x+2}{y-3}$$

Answer

$$\dfrac{x-2}{y-3}$$

Answer

$$\dfrac{x-2}{y+3}$$

Answer

$$\dfrac{x+2}{y+3}$$

Question 5

Simplify the following expression $$\dfrac{{{x}^{2}}+xy-2{{y}^{2}}}{{{x}^{3}}-{{y}^{3}}}$$

Accepted Answer

$$\dfrac{x+2y}{{{x}^{2}}+xy+{{y}^{2}}}$$

Answer

$$\dfrac{x-2y}{{{x}^{2}}-xy+{{y}^{2}}}$$

Answer

$$\dfrac{x-2y}{{{x}^{2}}+xy+{{y}^{2}}}$$

Answer

$$\dfrac{x+2y}{{{x}^{2}}-xy+{{y}^{2}}}$$