Simplify the equation.
[tex]\begin{gathered} \frac{x}{x+4}+\frac{4}{x-5}=\frac{36}{x^2-x-20} \\ \frac{x(x-5)+4(x+4)}{(x+4)(x-5)}=\frac{36}{x^2-x-20} \\ \frac{x^2-5x+4x+16}{x^2-5x+4x-20}=\frac{36}{x^2-x-20} \\ x^2-x+16=36 \end{gathered}[/tex]
Solve the equation for x.
[tex]\begin{gathered} x^2-x+16=36 \\ x^2-x+16-36=0 \\ x^2-x-20=0 \end{gathered}[/tex]
Factorize the equation for x.
[tex]\begin{gathered} x^2-5x+4x-20=0 \\ x(x-5)+4(x-5)=0 \\ (x+4)(x-5)=0 \\ x=-4,5 \end{gathered}[/tex]
So x = -4, 5.
