Question

If $\frac{3x+a}{x^2+3x+2}=\frac{A}{x-2}-\frac{10}{x-1}$, then $a=$... and $A=$ ...

• A. $a=7,A=13$
• B. $a=11,A=13$
• C. $a=13,A=7$
• D. $a=13,A=11$

Answer 1

The correct option is A $a=7,A=13$

$\frac{3x+a}{x^2-3x+2}=\frac{A}{x-2}-\frac{10}{x-1}=\frac{A}{x-2}+\frac{-10}{x-1}$
$\Rightarrow 3x+a=A(x-1)-10(x-2)$
On comparing coefficients we get
$A-10=3\Rightarrow A=13$ and $-A+20=a\Rightarrow a=7$
Hence, option 'A' is correct.