Question

resolve into partial fraction
2x+3/(x-1)^3​

Answer 1

I hope it will help you

The answer is x = 6/5

Answer 2

Concept:

Partial fraction - Fractions which are used in decompositiong of any rational expression.

Given: Rsolve into partial fraction 2x+3/(x-1)³

Step by step process:

2x+3/(x-1)³ = A/(x-1) + B/(x-1)²+C/(x-1)³

Or, 2x+3/(x-1)³ = A(x-1)²+ B(x-1)+ C /(X-1)³

Or, 2x+3 = A(x²-2x + 1) + B (x-1)+C          (a+b)²= a²-2ab+b²

               =Ax²-2Ax+A+Bx-B+C

Coefficient x²         Coefficient x             Coefficient

A= 0                        -2A+B=2                    -B+C=3

                           Or,-2(0) + B = 2         Or, -2 + C =3  

                                     B=2                            C=5  

2x3/(x-1)³= 0/(x-1)+2/(x-1)²+5/(x-1)³

Answer:  2x3/(x-1)³=  2/(x-1)²+5/(x-1)³

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