Rational expressions and equations Quiz 1

Question 1

Simplify: $$\dfrac{\dfrac{6{{x}^{2}}+17x+5}{2{{x}^{3}}+5{{x}^{2}}}}{\dfrac{{{x}^{4}}-{{x}^{3}}}{3{{x}^{2}}-2x-1}}$$

Accepted Answer

$$\dfrac{\left(3x+1\right)^2}{x^5}$$

Answer

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

Answer

$$x$$

Answer

$$\dfrac{x^5}{\left(3x+1\right)^2}$$

Question 2

Simplify:$$\dfrac{\dfrac{9}{a}-\dfrac{9}{{{a}^{2}}}}{\dfrac{3}{a}-\dfrac{6}{{{a}^{2}}}+\dfrac{3}{{{a}^{3}}}}-\dfrac{\dfrac{12}{{{a}^{2}}}+\dfrac{12}{a}}{4-\dfrac{4}{{{a}^{2}}}}$$

Accepted Answer

$$3$$

Answer

$$a+1$$

Answer

$$4(a+1)$$

Answer

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

Question 3

Simplify: $$\dfrac{\dfrac{27{{x}^{5}}}{2}+4{{x}^{2}}{{y}^{3}}+27{{x}^{4}}y+18{{x}^{3}}{{y}^{2}}}{{{x}^{2}}{{(3x+2y)}^{3}}}$$

Accepted Answer

$$\dfrac{1}{2}$$

Answer

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

Answer

2x

Answer

2

Question 4

Solve for x:$$\dfrac{2}{x+4}-\dfrac{2}{x+7}=\dfrac{6}{x-11}-\dfrac{6}{x+4}$$.

Accepted Answer

$$\dfrac{-58}{7}$$

Answer

$$-8$$

Answer

$$\dfrac{72}{7}$$

Answer

$$-42$$

Question 5

If $$t+\dfrac{1}{t}=2$$ then find the value of $$\dfrac{{{t}^{3}}+{{t}^{2}}+\dfrac{1}{{{t}^{3}}}+\dfrac{1}{{{t}^{2}}}}{{{t}^{4}}+\dfrac{1}{{{t}^{4}}}}$$.

Accepted Answer

$$2$$

Answer

$$4$$

Answer

$$1$$

Answer

$$3$$