Question

Solve: If there are multiple solutions, list them separated by commas, e.g. x=1,2. If there is no solution, enter ∅.

Answer 1

Simplify the equation.

`\begin{gathered} (x)/(x+4)+(4)/(x-5)=(36)/(x^2-x-20) \\ (x(x-5)+4(x+4))/((x+4)(x-5))=(36)/(x^2-x-20) \\ (x^2-5x+4x+16)/(x^2-5x+4x-20)=(36)/(x^2-x-20) \\ x^2-x+16=36 \end{gathered}`

Solve the equation for x.

`\begin{gathered} x^2-x+16=36 \\ x^2-x+16-36=0 \\ x^2-x-20=0 \end{gathered}`

Factorize the equation for x.

`\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}`

So x = -4, 5.