Question

Solve for all values of x:
start fraction, x, divided by, x, plus, 3, end fraction, minus, 2, equals, minus, start fraction, 3, divided by, x, plus, 3, end fraction
x+3
x
​
−2=−
x+3
3

Answer 1

Interpret the equation as
x/(x+3) − 2 = −3/(x+3), with x ≠ −3.

Bring the fraction on the right to the left:
x/(x+3) + 3/(x+3) − 2 = 0
⇒ (x+3)/(x+3) − 2 = 0
⇒ 1 − 2 = 0, which is false.

Equivalently, multiplying both sides by x+3 gives −x − 6 = −3 ⇒ x = −3, but x = −3 is not allowed (denominator 0). Hence there is no solution.

Solution set: ∅.