Decompose into partial fractions.

Answer

We need to find *A* and *B* so that

Adding the partial fractions,

We must have the numerators equal, so we need to find *A* and *B* such that

10*x* + 27 = *A*(*x* + 3) + *B*(*x* + 2).

Take *x* = -3 so we can find *B* without worrying about *A*:

10*x* + 27 = *A*(*x* + 3) + *B*(*x* + 2)

10(-3) + 27 = *A*((-3) + 3) + *B*((-3) + 2)

-3 = -*B*

*B* = 3.

Now take *x* = 0 and find *A*:

10*x* + 27 = *A*(*x* + 3) + *B*(*x* + 2)

10(0) + 27 =* A*((0) + 3) + (3)((0) + 2)

27 = 3*A* + 6

7 = *A*

The final decomposition is