2. Simplify the expression: (x + 3) / (x^2 + 4x - 21) - (x + 1) / (2x - 6)

Question

a. (-x^2 - 6x -1) / (2x^2 + 8x - 42)
b. (-x^2 + 10x + 13) / (2x^2 + 8x - 42)
c. (-x^2 - 6x + 13) / (2x^2 + 8x - 42)
d. (x^2 - 26x - 7) / (2x^2 + 8x - 42)

Answer 1

(x+3) / (x^2 + 4x - 21) - (x+1) / (2x-6)
(x+3) / (x+7)(x-3) - (x+1) / 2(x-3)
now use a common denominator, and you have
2(x+3) / 2(x+7)(x-3) - (x+1)(x+7) / 2(x-3)(x+7)
(2(x+3) - (x+1)(x+7)) / 2(x-3)(x+7)
(-x^2-6x-1) / (2x^2+8x-42)