Factor out the common term \(x\).
\[l\imath mx->2\times \frac{x(x+2)}{{x}^{2}-x-6}\]
Factor \({x}^{2}-x-6\).
Ask: Which two numbers add up to \(-1\) and multiply to \(-6\)?
Rewrite the expression using the above.
\[(x-3)(x+2)\]
\[l\imath mx->2\times \frac{x(x+2)}{(x-3)(x+2)}\]
Cancel \(x+2\).
\[l\imath mx->2\times \frac{x}{x-3}\]
Simplify \(2\times \frac{x}{x-3}\) to \(\frac{2x}{x-3}\).
\[l\imath mx->\frac{2x}{x-3}\]
Regroup terms.
\[-+l\imath mx>\frac{2x}{x-3}\]
Divide both sides by \(\imath \).
\[-+lmx>\frac{\frac{2x}{x-3}}{\imath }\]
Simplify \(\frac{\frac{2x}{x-3}}{\imath }\) to \(\frac{2x}{\imath (x-3)}\).
\[-+lmx>\frac{2x}{\imath (x-3)}\]
Divide both sides by \(m\).
\[-+lx>\frac{\frac{2x}{\imath (x-3)}}{m}\]
Simplify \(\frac{\frac{2x}{\imath (x-3)}}{m}\) to \(\frac{2x}{\imath m(x-3)}\).
\[-+lx>\frac{2x}{\imath m(x-3)}\]
Divide both sides by \(x\).
\[-+l>\frac{\frac{2x}{\imath m(x-3)}}{x}\]
Simplify \(\frac{\frac{2x}{\imath m(x-3)}}{x}\) to \(\frac{2x}{\imath mx(x-3)}\).
\[-+l>\frac{2x}{\imath mx(x-3)}\]
Cancel \(x\).
\[-+l>\frac{2}{\imath m(x-3)}\]
Multiply both sides by \(-1\).
\[l<-\frac{2}{\imath m(x-3)}\]
l<-2/(IM*m*(x-3))
