Question

Solve for all values of x:
minus, start fraction, 3, divided by, x, plus, 7, end fraction, plus, 9, equals, minus, start fraction, x, divided by, x, plus, 7, end fraction
−
x+7
3
​
+9=−
x+7
x

Answer 1

Solve the equation
-3/(x+7) + 9 = -x/(x+7), with x ≠ -7.

Multiply both sides by (x+7):
-3 + 9(x+7) = -x

Expand and simplify:
-3 + 9x + 63 = -x
9x + 60 = -x
10x + 60 = 0
x = -6

Check: x = -6 is allowed (not -7) and satisfies the original equation.

Answer: x = -6.