Solve for A:
5/(x^2+6 x+8) = A/(x+2)+B/(x+4)
5/(x^2+6 x+8) = A/(x+2)+B/(x+4) is equivalent to A/(x+2)+B/(x+4) = 5/(x^2+6 x+8):
A/(x+2)+B/(x+4) = 5/(x^2+6 x+8)
Subtract B/(x+4) from both sides:
A/(x+2) = 5/(x^2+6 x+8)-B/(x+4)
Multiply both sides by x+2:
Answer: |A = (5 (x+2))/(x^2+6 x+8)-(B (x+2))/(x+4)
Solve for B:
5/(x^2+6 x+8) = A/(x+2)+B/(x+4)
5/(x^2+6 x+8) = A/(x+2)+B/(x+4) is equivalent to A/(x+2)+B/(x+4) = 5/(x^2+6 x+8):
A/(x+2)+B/(x+4) = 5/(x^2+6 x+8)
Subtract A/(x+2) from both sides:
B/(x+4) = 5/(x^2+6 x+8)-A/(x+2)
Multiply both sides by x+4:
Answer: |B = (5 (x+4))/(x^2+6 x+8)-(A (x+4))/(x+2)
IF YOU WISH TO SOLVE FOR NUMERICAL VALUES OF A AND B, THEN SOLVE FOR X FIRST AND SUBSTITUTE:
Solve for x:
x^2+6 x+8 = 0
The left hand side factors into a product with two terms:
(x+2) (x+4) = 0
Split into two equations:
x+2 = 0 or x+4 = 0
Subtract 2 from both sides:
x = -2 or x+4 = 0
Subtract 4 from both sides:
Answer: |x = -2 or x = -4
