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