Question

4/x-2 - 2x-3/x²-4 = 5/x+2

Answer 1

Find x

`\begin{gathered} (4)/(x-2)-(2x-3)/(x^2-4)=(5)/(x+2) \\ \end{gathered}`

Solve the substraction of fractions

`(4\ast(x+2)-(2x-3))/(x^2-4)=(5)/(x+2)`

Factorize the denominator and solve

`\begin{gathered} (4\ast(x+2)-(2x-3))/((x+2)(x-2))=(5)/(x+2) \\ (x+2\ast(4\ast(x+2)-(2x-3)))/((x+2)\ast(x-2))=5 \\ (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=(-21)/(-3) \\ x=7 \end{gathered}`