Question

Classify the solutions of 3 over x plus 5, plus one fifth, equals 2 over x plus 5 as extraneous or non-extraneous.

x = −5; extraneous
x = −5; non-extraneous
x = −10; extraneous
x = −10; non-extraneous

Answer 1

3/(x + 5) + 1/5 = 2/(x + 5)

1/(x + 5) + 1/5 = 0

1/(x + 5) = -1/5

5 = -(x + 5)

5 = -x - 5

10 = -x

x = -10

x = - 10; non-extraneous