Question

4x-5/1-6x = x+10/x-6

your help would be much appreciated

Answer 1

(4x - 5) / (1 - 6x)=(x + 10) / (x -6),
Multiply both sides by x - 6 and get:
(x - 6) (4x - 5) / (1 - 6x) = (x + 10),
Cross multiply:
(x - 6) (4x - 5) = (x + 10) (1 - 6x),
Remove pqarentheses by multiplication:
4x^2 - 5x -24x + 30=x - 6x^2 + 10 -60x,
Combine luike terms:
4x^2 - 29x + 30 = -6x^2 -59x + 10,
Transpose all variables to left side
and all constants to right side,
4x^2 - 29x +6x^2 + 59x = 10 - 30,
Combine like-terms:
10x^2 + 30x = -20,
10x^2 + 30x + 20 = 0,
Divide both sides by 10 & get:
x^2 + 3x + 2 = 0,
Factor the trinomial:
(x + 1) (x + 2) = 0.

x + 1 = 0,
x = -1.

x + 2 = 0,
x = -2.

Solution set: x = -1, and x = -2.