Question

Solve for x and simplify the answer fully.
start fraction, 3, divided by, x, plus, 1, end fraction, equals, start fraction, 5, divided by, 5, x, minus, 5, end fraction
x+1
3
​
=
5x−5
5

Answer 1

We have 3/(x+1) = 5/(5x−5). Note 5x−5 = 5(x−1), so the equation is equivalently 3/(x+1) = 1/(x−1).

Cross-multiply: 3(x−1) = 1(x+1) → 3x − 3 = x + 1 → 2x = 4 → x = 2.

Check domain: x ≠ −1 and x ≠ 1 (would make a denominator zero). x = 2 is allowed, so the solution is x = 2.