Question

How would I solve these problem?

4/x-1 = 10/1
and
x/x-8 = x / 24

Answer 1

1. 4/(x-1) = 10/1.
Invert both sides:
(x-1)/4 = 1/10
Multiply both sides by 40:
10(x-1) = 4.
10x - 10 = 4.
10x = 14.
X = 14/10 = 7/5.

2. x/(x-8) = x/24.
Multiply both sides by 24:
24x/(x-8) = x.
Cross multiply:
x(x-8) = 24x.
x^2 -8x = 24x.
x^2 - 8x - 24x = 0.
x^2 - 32x = 0.
x(x-32) = 0.

X = 0.

x-32 = 0.
X = 32.

Solution set: X = 0, and X = 32.

Answer 2

8x24