Question

Separate $\frac{5x-11}{2x^2+x-6}$ into partial fractions

• A. $\frac{-3}{x+2}+\frac{1}{x-3}$
• B. $\frac{3}{x+2}-\frac{1}{2x-3}$
• C. $\frac{1}{x+2}-\frac{3}{2x-3}$
• D. $\frac{5x}{x-2}-\frac{-1}{2x-3}$

Answer 1

The correct option is B $\frac{3}{x+2}-\frac{1}{2x-3}$

Let $\frac{5x-11}{2x^2+x-6}=\frac{5x-11}{(x+2)(2x-3)}=\frac{A}{(x+2)}+\frac{B}{(2x-3)}$ ....(1)

Multiply $(x+2)(2x-3)$ on both the sides, we get

$5x-11=A(2x-3)+B(x+2)$

Put $x=-2$ to find value of A

$\therefore 5(-2)-11=A\left[2\right(-2)-3]\Rightarrow A=3$

Now put $x=\frac{3}{2}$ to find value of B

$\therefore 5\left(\frac{3}{2}\right)-11=B(\frac{3}{2}+2)\Rightarrow B=-1$

Substitute the values of A and B,

$\frac{5x-11}{2x^2+x-6}=\frac{3}{(x+2)}-\frac{1}{(2x-3)}$