Question

resolve the following partial fractions: 2x + 3/(x-2) (x+5)​

Answer 1

Solution

Given :-

• Fraction , (2x+3)/(x-2)(x+5)

Find :-

• Partial fraction of given faction

Explanation

First let,

➡ (2x+3)/(x-2)(x+5) = A/(x-2) + B/(x+5) __(1)

Multiply by (x-2) (x+5) both side.

➡(2x+3) = A(x+5) + B(x-2)

➡(2x+3) = (A+B)x + 5A - 2B _____(2)

Compare coefficient of x from both side

➡ A + B = 2 ,_____________(3)

Again, compare constant part.

➡5A - 2B = 3 ____________(4)

Now, multiply by 2 in equ(3)

➡2A + 2B = 4_________(5)

Add equ(4) & equ(5)

➡7A = 7

➡A = 7/7

➡A = 1

Keep in equ(4)

➡ 5×1 - 2B = 3

➡B = 5 - 3

➡B = 2

By equ(1)

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

Hence

• partial fraction will be of given fraction = 1/(x-2) + 2/(x+2)

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