Question

Solve for x and simplify the answer fully.
start fraction, 3, divided by, 5, x, minus, 3, end fraction, equals, start fraction, 5, divided by, x, plus, 9, end fraction
5x−3
3
​
=
x+9
5

Answer 1

Solve 3/(5x − 3) = 5/(x + 9).

Cross-multiply:
3(x + 9) = 5(5x − 3)
3x + 27 = 25x − 15

Bring x-terms to one side:
27 + 15 = 25x − 3x
42 = 22x
x = 42/22 = 21/11

Check denominators: 5x − 3 ≠ 0 ⇒ x ≠ 3/5, and x + 9 ≠ 0 ⇒ x ≠ −9. x = 21/11 is allowed.

Answer: x = 21/11.