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