Question

Solve for all values of x:
start fraction, 5, x, divided by, x, minus, 3, end fraction, minus, 1, equals, minus, start fraction, 1, divided by, x, minus, 3, end fraction
x−3
5x
​
−1=−
x−3
1

Answer 1

Solve (5x)/(x−3) − 1 = −1/(x−3), with x ≠ 3.

Multiply both sides by (x−3):
5x − (x−3) = −1

Simplify:
5x − x + 3 = −1
4x + 3 = −1
4x = −4
x = −1

Check: for x = −1, left side (5(−1))/(−4) − 1 = (−5)/(−4) − 1 = 5/4 − 1 = 1/4, right side −1/(−4) = 1/4. Works.

Answer: x = −1.