Precal Help? Partial Fractions?

Question

Determine the constants (denoted by capital letters) so that the equation is an identity. Use either the equating-the-coefficients theorem, as in Example 1, the convenient-values method that was explained after Example 1, or a combination.

 

5 − x

(7x + 8)2

 = 

A

7x + 8

 + 

B

(7x + 8)2

 

A = 
B = 

Answer 1

Equate the x  coefficients.

Equate the constants.

From the equation (1)

Substitute  -1/7 for A   in equation (2).

Therfore, the partial decomposition is

Therfore ,