Question

resolve into partial fraction 2x+5/(x+2)(x+3)​

Answer 1

Step-by-step explanation:

Answer

Let

(2x - 5) (x+3)(x + 1)2

C

(x + 1)?

► 2x – 5 = A(x+1) +

A x + 3 + B x+1 +

B (x+1)(x+3)+C(x+3)

> 2x – 5 = A (x2 + 2x+1)+ B (x² + 4x + 3) + C (x+3)

On comparing coefficients

0 = A + B, 2 = 2A + 4B + C,-5 = A + 3B + 3C

A = 11 4 B 11 6. С 7 2

(2x – 5) (x+3)(x + 1)? 7 4(x + 1) 2(x + 1)?

Answer 2

Step-by-step explanation:

2x+5/(x+2)(x+3) = A/(x+2) + B/(x+3)

2x+5/(x+2)(x+3)=A(x+3) + B(x+2)/(x+2)(x+3)

now cancle (x+2)(x+3) both sides.

2x+5 = A(x+3) + B(x+2)

Now put x = -2

2(-2)+5 = A(-2+3) + B(-2+2)

5-4 = A(1) + B(0)

1 = A + 0

A = 1.

NOW put X= -3

THEN

2(-3)+5 = A(-3+3) + B(-3+2)

5-6 (or) -6+5 = A(0) + B(2-3)

-1 = 0+B(-1)

-1 = -B

B=1.

2x+5 = 1/(x+2) + (-1/(x+3))

2x+5 = 1/(x+2) +-1/(x+3).