Help please. the answer of this is 5/8 just can't seem to figure out how to factor out the problem?

Question

Divide:
x^2 – 3x + 2/8x - 8 ÷ x^2 – 4/5x +10. PLease help

Answer 1

I'm going to assume the placement of parenthesis.
(x^2 – 3x + 2)/(8x - 8) ÷ (x^2 – 4)/(5x +10)

Step 1: Flip the second fraction, so that you have multiplication instead of division.
(x^2 – 3x + 2)/(8x - 8) * (5x +10)/(x^2 – 4)

Step 2: Factor.
x^2 – 3x + 2 = (x - 2)(x - 1)
8x - 8 = 8(x-1)
5x +10 = 5(x + 2)
x^2 – 4 = for a^2 - b^2, the factors are (a + b)(a - b). So: (x + 2)(x -2)

(x - 2)(x - 1) / 8(x-1) * 5(x + 2) / (x + 2)(x -2)

Step 3: Cancel out, multiply
(x - 2) / 8 * 5 / (x -2)
5 / 8 (solution!)