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Nataly [62]
3 years ago
5

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

Business
1 answer:
Volgvan3 years ago
5 0

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} .

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