Answer:
[tex]x=-\frac{17}{3}[/tex]
Step-by-step explanation:
we have
[tex]\frac{4}{x-3}+\frac{2}{x^{2}-9}=\frac{1}{x+3}[/tex]
Solve for x
Applying difference of squares in the denominator of the second term in the left side
[tex]\frac{4}{x-3}+\frac{2}{(x+3)(x-3)}=\frac{1}{x+3}[/tex]
Multiply both sides by (x+3)(x-3)
[tex]4(x+3)+2=(x-3)[/tex]
Apply the distributive property in the left side
[tex]4x+12+2=x-3[/tex]
Combine like terms left side
[tex]4x+14=x-3[/tex]
Group terms
[tex]4x-x=-3-14[/tex]
[tex]3x=-17[/tex]
Divide by 3 both sides
[tex]x=-\frac{17}{3}[/tex]
