How do you express x+1(x2)(x1) in partial fractions?

1 Answer

x+1x2(x1)=1x22x+2x1

Explanation:

From the given x+1x2(x1), we set up the equations with the needed unknown constants represented by letters

x+1x2(x1)=Ax2+Bx+Cx1

The Least Common Denominator is x2(x1).

Simplify

x+1x2(x1)=Ax2+Bx+Cx1

x+1x2(x1)=A(x1)+B(x2x)+Cx2x2(x1)

Expand the numerator of the right side of the equation

x+1x2(x1)=AxA+Bx2Bx+Cx2x2(x1)

Rearrange from highest degree to the lowest degree the terms of the numerator at the right side

x+1x2(x1)=Bx2+Cx2+AxBxAx2(x1)

Now let us fix the numerators on both sides so that the numerical coefficients are matched.

0x2+1x+1x0x2(x1)=(B+C)x2+(AB)xAx0x2(x1)

We can now have the equations to solve for A, B, C

B+C=0
AB=1
A=1

Simultaneous solution results to
A=1
B=2
C=2

We now have the final equivalent
x+1x2(x1)=1x22x+2x1

God bless....I hope the explanation is useful.