Decompose into partial fractions.

Answer

The denominator factors nicely into

2*x*^{2} + 14*x* = 2*x*(*x* + 7)

so the decomposition will look like

Add the partial fractions and set the resulting numerator equal to the original numerator:

15*x* + 21 = *A*(*x* + 7) + *B*(2*x*).

Set *x* = 0 and find *A*:

15*x* + 21 = *A*(*x* + 7) + *B*(2*x*)

15(0) + 21 = *A*(0 + 7) + *B*(2(0))

21 = 7*A*

3 = *A*

Set *x* = 1 and find *B*:

15*x* + 21 = *A*(*x* + 7) + *B*(2*x*)

15(1) + 21 = (3)(1 + 7) + *B*(2(1))

36 = 24 + 2*B*

6 = *B*

The decomposition is