Partial fraction decomposition Quiz 1

Question 1

Decompose the fraction: $$\dfrac{x-7}{{{x}^{2}}+2x-3}$$

Accepted Answer

$$\dfrac{1}{2}\left[ \dfrac{-3}{(x-1)}+\dfrac{5}{(x+3)} \right]$$

Answer

$$\dfrac{1}{2}\left[ \dfrac{3}{(x-1)}-\dfrac{5}{(x+3)} \right]$$

Answer

$$\dfrac{1}{2}\left[ \dfrac{-5}{(x-1)}+\dfrac{7}{(x+3)} \right]$$

Answer

$$\dfrac{1}{2}\left[ \dfrac{-3}{(x-1)}+\dfrac{5}{2(x+3)} \right]$$

Question 2

Find the partial fraction decomposition for: $$\dfrac{3{{x}^{2}}-4x+5}{{{x}^{3}}-5{{x}^{2}}}$$

Accepted Answer

$$\dfrac{3}{5x}-\dfrac{1}{{{x}^{2}}}+\dfrac{12}{5(x-5)}$$

Answer

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

Answer

$$\dfrac{3}{5x}-\dfrac{1}{{{x}^{2}}}-\dfrac{12}{5(x-5)}$$

Answer

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

Question 3

Find the partial fraction decomposition for: $$-\dfrac{24{{x}^{2}}+32x+9}{16{{x}^{3}}+24{{x}^{2}}+9x}$$

Accepted Answer

$$-\dfrac{1}{x}-\dfrac{2}{(4x+3)}-\dfrac{2}{{{(4x+3)}^{2}}}$$

Answer

$$-\dfrac{1}{x}-\dfrac{2}{(4x+3)}-\dfrac{1}{{{(4x+3)}^{2}}}$$

Answer

$$\dfrac{1}{x}-\dfrac{2}{(4x+3)}-\dfrac{2}{{{(4x+3)}^{2}}}$$

Answer

$$-\left[ \dfrac{1}{x}-\dfrac{2}{(4x+3)}-\dfrac{2}{{{(4x+3)}^{2}}} \right]$$

Question 4

Find the value of $$A+B+C$$ where: $$\dfrac{3{{x}^{2}}+5x-16}{x(2x+1)(x-4)}=\dfrac{A}{x}+\dfrac{B}{(2x+1)}+\dfrac{C}{(x-4)}$$

Accepted Answer

$$\dfrac{50}{9}$$

Answer

$$\dfrac{10}{9}$$

Answer

8

Answer

14

Question 5

Find the value of E such that $$A+B+C+D+E=0$$ and $$\dfrac{16}{({{x}^{2}}+x+2){{(x-1)}^{2}}}=\dfrac{Ax+B}{{{x}^{2}}+x+2}+\dfrac{C}{(x-1)}+\dfrac{D}{{{(x-1)}^{2}}}$$

Accepted Answer

-6

Answer

-4

Answer

6

Answer

8