Question

Resolve into partial fraction $\frac{2x^2+5x-11}{x^2+2x-3}$

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

Answer 1

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

Let $I=\frac{2x^2+5x-11}{x^2+2x-3}=\frac{2(x^2+2x-3)+x-5}{x^2+2x-3}$
$=2+\frac{x-5}{x^2+2x-3}=2+\frac{x-5}{(x+3)(x-1)}$
Now $\frac{x-5}{(x+3)(x-1)}=\frac{A}{(x-1)}+\frac{B}{(x+3)}$
$\Rightarrow x-5=A(x+3)+B(x-1)$
On comparing coefficients we get
$1=A+B,-5=3A-B\Rightarrow A=-1,B=2$
Therefore
$I=2-\frac{1}{x-1}+\frac{2}{x+3}$
Hence, option 'B' is correct.