Question

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

Answer 1

Interpret the equation as 9 + x/(x+1) = −1/(x+1). Domain: x ≠ −1.

Multiply both sides by x+1:
9(x+1) + x = −1
9x + 9 + x = −1
10x + 9 = −1
10x = −10
x = −1

But x = −1 is excluded (denominator zero), so there is no solution.

If you meant a different placement of parentheses (e.g. 9 + (x+1)/x = −(x+1) or 9 + x/(x+1) = −(x+1)), tell me which form and I’ll solve that.