Review the work showing the first few steps in writing a partial fraction decomposition.

StartFraction 4 x + 40 Over (x + 2) (x + 6) EndFraction = StartFraction A Over x + 2 EndFraction + StartFraction 16 Over x + 6 EndFraction

4x + 40 = A(x + 6) + B(x + 2)

4x + 40 = Ax + 6A + Bx + 2B

What is the partial fraction decomposition in terms of x?

StartFraction 4 x + 40 Over (x + 2) (x + 7) EndFraction = StartFraction negative 12 Over x + 2 EndFraction + StartFraction 16 Over x + 6 EndFraction

StartFraction 4 x + 40 Over (x + 2) (x + 7) EndFraction = StartFraction negative 4 Over x + 2 EndFraction + StartFraction 8 Over x + 6 EndFraction

StartFraction 4 x + 40 Over (x + 2) (x + 7) EndFraction = StartFraction 8 Over x + 2 EndFraction + StartFraction negative 4 Over x + 6 EndFraction

StartFraction 4 x + 40 Over (x + 2) (x + 7) EndFraction = StartFraction 16 Over x + 2 EndFraction + StartFraction negative 12 Over x + 6 EndFraction

The Answer is C

StartFraction 4 x + 40 Over (x + 2) (x + 7) EndFraction = StartFraction 8 Over x + 2 EndFraction + StartFraction negative 4 Over x + 6 EndFraction

What is partial fraction?

Partial fractions are the fractions used for the decomposition of a rational expression.

Given:

(4x + 40)/ (x + 2)(x + 6) = A/(x + 2) + B/(x + 6)

4x + 40 = A(x + 6) + B(x + 2)

4x + 40 = x(A+B) + 6A +2B

On comparing

4= A+B

A= 4-B

and, 6A +2B =40

3A + B =20

3(4-B) + B =20

12 - 3B + B =20

-2B = 8

B= -4

and, A= 8

Hence, StartFraction 4 x + 40 Over (x + 2) (x + 7) EndFraction = StartFraction 8 Over x + 2 EndFraction + StartFraction negative 4 Over x + 6 EndFraction

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