Question

Simplify each expression and state any non-permissible values. (5 marks - show your work)

(3x+1)/(2x^2-2) + (2x+2)/(2x^2-8x+6)

Please help me!

Answer 1

(3x+1)/2(x^2-1) + 2(x+1)/2(x^2-4x+3) =
(3x+1)/2(x+1)(x-1) + 2(x+1)/2(x-1)(x-3) = (3x+1)/2(x+1)(x-1) + (x+1)/(x-1)(x-3)
LCD = 2(x+1)(x-1)(x-3)

(3x+1)(x-3)/2(x+1)(x-1)(x-3) +
(x+1)(x+1)/2(x+1)(x-1)(x-3)

(3x^2-9x+x-3)/LCD + (x^2+2x+1)/LCD

Add the Numerators:
(4x^2-6x-2)/LCD = 2(2x^2-3x-1)/LCD =
2(2x^2-3x-1)/2(x+1)(x-1)(x-3) =
(2x^2-3x-1)/(x+1)(x-1)(x-3)
The numerator cannot be factored.