Factor out the common term \(2\).
\[l\imath mx->2\times \frac{2({x}^{2}-4)}{x-2}\]
Rewrite \({x}^{2}-4\) in the form \({a}^{2}-{b}^{2}\), where \(a=x\) and \(b=2\).
\[l\imath mx->2\times \frac{2({x}^{2}-{2}^{2})}{x-2}\]
Use Difference of Squares: \({a}^{2}-{b}^{2}=(a+b)(a-b)\).
\[l\imath mx->2\times \frac{2(x+2)(x-2)}{x-2}\]
Cancel \(x-2\).
\[l\imath mx->2\times 2(x+2)\]
Simplify \(2\times 2(x+2)\) to \(4(x+2)\).
\[l\imath mx->4(x+2)\]
Regroup terms.
\[-+l\imath mx>4(x+2)\]
Divide both sides by \(\imath \).
\[-+lmx>\frac{4(x+2)}{\imath }\]
Rationalize the denominator: \(\frac{4(x+2)}{\imath } \cdot \frac{\imath }{\imath }=-4(x+2)\imath \).
\[-+lmx>-4(x+2)\imath \]
Regroup terms.
\[-+lmx>-4\imath (x+2)\]
Divide both sides by \(m\).
\[-+lx>-\frac{4\imath (x+2)}{m}\]
Divide both sides by \(x\).
\[-+l>-\frac{\frac{4\imath (x+2)}{m}}{x}\]
Simplify \(\frac{\frac{4\imath (x+2)}{m}}{x}\) to \(\frac{4\imath (x+2)}{mx}\).
\[-+l>-\frac{4\imath (x+2)}{mx}\]
Multiply both sides by \(-1\).
\[l<\frac{4\imath (x+2)}{mx}\]
l<(4*IM*(x+2))/(m*x)
