Multiply both sides by the Least Common Denominator: \(x(x+5)\).
\[(x+1)(x+5)-3x-5=x(x+4)\]
Simplify.
\[{x}^{2}+3x={x}^{2}+4x\]
Cancel \({x}^{2}\) on both sides.
\[3x=4x\]
Move all terms to one side.
\[3x-4x=0\]
Simplify \(3x-4x\) to \(-x\).
\[-x=0\]
Multiply both sides by \(-1\).
\[x=0\]
Check solution
When \(x=0\), the original equation \(\frac{x+1}{x}-\frac{3x+5}{{x}^{2}+5x}=\frac{x+4}{x+5}\) does not hold true.We will drop \(x=0\) from the solution set.
