Question

Resolve (7x+19)/(x+1)(x+5) into partial fraction​

Answer 1

Answer:

$\dfrac{7x+19}{(x+1)(x+5)}=\dfrac{3}{x+1}+\dfrac{4}{x+5}$

Explanation:

The given expression is  

$\dfrac{7x+19}{(x+1)(x+5)}$

We need to resolve this into partial fraction.

The form of the partial fraction decomposition is

$\dfrac{7x+19}{(x+1)(x+5)}=\dfrac{A}{x+1}+\dfrac{B}{x+5}$        ...(1)

$\dfrac{7x+19}{(x+1)(x+5)}=\dfrac{A(x+5)+B(x+1)}{(x+1)(x+5)}$

$7x+19=Ax+5A+Bx+B$

$7x+19=(A+B)x+(5A+B)$

On comparing both sides, we get

$A+B=7$      ...(2)

$5A+B=19$    ...(3)

Subtract (2) from (3), we get

$4A=12$

$A=3$

Put A=3 in (1).

$3+B=7$

$B=4$

Put A=3 and B=4 in (1).

$\dfrac{7x+19}{(x+1)(x+5)}=\dfrac{3}{x+1}+\dfrac{4}{x+5}$

Therefore, $\dfrac{7x+19}{(x+1)(x+5)}=\dfrac{3}{x+1}+\dfrac{4}{x+5}$ .