Find x
[tex]\begin{gathered} \frac{4}{x-2}-\frac{2x-3}{x^2-4}=\frac{5}{x+2} \\ \end{gathered}[/tex]Solve the substraction of fractions
[tex]\frac{4\ast(x+2)-(2x-3)}{x^2-4}=\frac{5}{x+2}[/tex]Factorize the denominator and solve
[tex]\begin{gathered} \frac{4\ast(x+2)-(2x-3)}{(x+2)(x-2)}=\frac{5}{x+2} \\ \frac{x+2\ast(4\ast(x+2)-(2x-3))}{(x+2)\ast(x-2)}=5 \\ \frac{4\ast(x+2)-(2x-3)}{x-2}=5 \\ 4\ast(x+2)-(2x-3)=5\ast(x-2) \\ 4x+8-2x+3=5x-10 \\ 2x+11=5x-10 \\ 2x-5x=-10-11 \\ -3x=-21 \\ x=\frac{-21}{-3} \\ x=7 \end{gathered}[/tex]