Rewrite \({x}^{2}-9\) in the form \({a}^{2}-{b}^{2}\), where \(a=x\) and \(b=3\).
\[l\imath mx->3\times \frac{{x}^{2}-{3}^{2}}{x-3}\]
Use Difference of Squares: \({a}^{2}-{b}^{2}=(a+b)(a-b)\).
\[l\imath mx->3\times \frac{(x+3)(x-3)}{x-3}\]
Cancel \(x-3\).
\[l\imath mx->3(x+3)\]
Regroup terms.
\[-+l\imath mx>3(x+3)\]
Divide both sides by \(\imath \).
\[-+lmx>\frac{3(x+3)}{\imath }\]
Rationalize the denominator: \(\frac{3(x+3)}{\imath } \cdot \frac{\imath }{\imath }=-3(x+3)\imath \).
\[-+lmx>-3(x+3)\imath \]
Regroup terms.
\[-+lmx>-3\imath (x+3)\]
Divide both sides by \(m\).
\[-+lx>-\frac{3\imath (x+3)}{m}\]
Divide both sides by \(x\).
\[-+l>-\frac{\frac{3\imath (x+3)}{m}}{x}\]
Simplify \(\frac{\frac{3\imath (x+3)}{m}}{x}\) to \(\frac{3\imath (x+3)}{mx}\).
\[-+l>-\frac{3\imath (x+3)}{mx}\]
Multiply both sides by \(-1\).
\[l<\frac{3\imath (x+3)}{mx}\]
l<(3*IM*(x+3))/(m*x)
