SOLUTION: Could you please help me solve this equation for A, B, and C. 11x^2-x+8/(x+1)(X^2+4)=A/(x+1)+Bx+C/X^2+4

Question 151438: Could you please help me solve this equation for A, B, and C.
11x^2-x+8/(x+1)(X^2+4)=A/(x+1)+Bx+C/X^2+4
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Multiply every term by the LCD to clear the fractions.

Simplify

Rearrange the terms

FOIL

Distribute

Notice how the terms on the right side are and . So this means that and

Also, notice how the terms on the right side are and . So this means that and

Finally, the constant terms on the right side are and . So this means that

Start with the first equation.

Subtract A from both sides.

Move onto the second equation

Plug in

Subtract 11 from both sides.

Multiply both sides by 4.

Add this equation to equation #3

+
--------------

Simplify

Divide both sides by 5.

Go back to the third equation

Plug in

Add 8 to both sides.

Divide both sides by 4.

Move onto the first isolated equation

Plug in

Subtract

====================================================

So the value of the constants are

, , and

So this means that the equation is
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