Question

What is the solution to the rational equation x over x squared minus 9 minus 1 over x plus 3 equals 1 over 4x minus 12 ?

x = -9 over 7

x = 15

x = 15 over 7

x = 9

Answer 1

\[\frac{ x }{ x ^{2}-9 }-\frac{ 1 }{ x+3 }=\frac{ 1 }{ 4x-12 }\]
\[\frac{ x }{ (x-3)(x+3) }-\frac{ 1 }{ (x-3) }=\frac{ 1 }{ 4(x-3) }\]
multiply both sides by (x-3)
\[\frac{x}{(x+3)}-1=\frac{1}{4}\]
add 1 to both sides
\[\frac{x}{x+3}=1\frac{1}{4}\]
multiply both sides by (x+3)
\[x=3\frac{3}{4}+1\frac{1}{4}x\]
subtract \[1\frac{1}{4}x\] from both sides
\[-\frac{1}{4}x=3\frac{3}{4}\]
divide both sides by \[-\frac{1}{4}\]
x=-15
ik its not one of the choices but that is what I got