Answer:
x = -26
Step-by-step explanation:
[tex](f-g)(x)=\frac{4}{x-3}-\frac{3}{x+5}=\frac{3}{x^2 +2x-15} \\ \\ \frac{4(x+5)-3(x-3)}{x^2 +2x-15} \\ \\ =\frac{4x+20-3x+9}{x^2 +2x-15}=\frac{3}{x^2 +2x-15} \\ \\ \frac{x+29}{x^2 +2x-15}=\frac{3}{x^2+2x-15} \\ \\ x+29=3 \\ \\ x=-26[/tex]
This is in the domain of the equation, and is thus a solution.
