Decompose into partial fractions.

Answer

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

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

11 – 23*x* = *A*(2 – 5*x*) + *B*(1 – *x*).

Take *x* = 1 to solve for *A*:

11 – 23*x* = *A*(2 – 5x) + *B*(1 – *x*)

11 – 23(1) = *A*(2 – 5(1)) + *B*(1 – 1)

-12 = -3*A*

4 = *A*

Then take *x* = 0 and solve for *B*:

11 – 23*x* = *A*(2 – 5*x*) + *B*(1 – *x*)

11 – 23(0) = (4)(2 – 5(0)) + *B*(1 – 0)

11 = 8 + *B*

3 = *B*

We get the decomposition