Question

Solve for all values of x:
1, plus, start fraction, 5, divided by, x, plus, 5, end fraction, equals, minus, start fraction, 9, x, divided by, x, plus, 5, end fraction
1+
x+5
5
​
=−
x+5
9x

Answer 1

Solve 1 + 5/(x+5) = −9x/(x+5), with x ≠ −5.

Multiply both sides by (x+5):
(x+5) + 5 = −9x

Simplify:
x + 10 = −9x
10x = −10
x = −1

Check: 1 + 5/(−1+5) = 1 + 5/4 = 9/4; −9(−1)/(−1+5) = 9/4. Matches.

Answer: x = −1.