Precal Help?

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.

 

21x2 − 59x + 110

(3x − 5)(x2 + 5)

 = 

A

3x − 5

 + 

Bx + C

x2 + 5

 

A=

B=

C=

Answer 1

Equate the   coefficients

Equate the x  coefficients

Equate the  constants.

Now solve above three equations.

Multiply each side of equation (1) by negative 5.

To eliminate the A variable add equations (3) & (4).

Multiply each side of equation (2) by negative 3.

To eliminate the B variable add equations (5) & (6).

Substitute C value in equation (3).

Substitute A value in equation (1).

Substitute A, B and C in equation (i).