Question

question
solve for all values of x:
$-9 + \frac{1}{x+9} = -\frac{x}{x+9}$
answer attempt 1 out of 2
additional solution no solution
$x = $

Explanation:

Step1: Eliminate denominator

Multiply all terms by $x+9$ (where $x
eq -9$):
$$-9(x+9) + 1 = -x$$

Step2: Expand left-hand side

$$-9x - 81 + 1 = -x$$

Step3: Simplify constants

$$-9x - 80 = -x$$

Step4: Isolate x terms

$$-9x + x = 80$$

Step5: Combine like terms

$$-8x = 80$$

Step6: Solve for x

$$x = \frac{80}{-8} = -10$$

Step7: Verify validty

Check $x=-10$: denominator $x+9=-1
eq 0$, so it is valid.

Answer:

$x=-10$