Answer:
The correct answer is the last option x=9
Step-by-step explanation:
Step 1
First step is to factor out the denominators. This step is shown below,
[tex]\frac{x}{x^2-9} -\frac{1}{x+3} =\frac{1}{4x-12}\\\frac{x}{(x+3)(x-3)} -\frac{1}{x+3}=\frac{1}{4(x-3)}[/tex]
Step 2
The next step is to multiply both sides of the equation by [tex]4(x-3)(x+3)[/tex] and solve for x.
This process is shown below,
[tex]4(x+3)(x-3)\bigl[ \frac{x}{(x+3)(x-3)} -\frac{1}{(x+3)} \bigr]=4(x+3)(x-3)\bigl[\frac{1}{4(x-3)} \bigr]\\\implies 4x-4(x-3)=(x+3)\\\implies 4x-4x+12=x+3\\\implies 12=x+3\\\implies 12-3=x\\\implies 9=x[/tex]
The answer is [tex]x=9.[/tex]
