Split the second term in \(2{x}^{2}-x-15\) into two terms.
Multiply the coefficient of the first term by the constant term.
\[2\times -15=-30\]
Ask: Which two numbers add up to \(-1\) and multiply to \(-30\)?
Split \(-x\) as the sum of \(5x\) and \(-6x\).
\[2{x}^{2}+5x-6x-15\]
\[l\imath mx->3\times \frac{2{x}^{2}+5x-6x-15}{3{x}^{2}+x-30}\]
Factor out common terms in the first two terms, then in the last two terms.
\[l\imath mx->3\times \frac{x(2x+5)-3(2x+5)}{3{x}^{2}+x-30}\]
Factor out the common term \(2x+5\).
\[l\imath mx->3\times \frac{(2x+5)(x-3)}{3{x}^{2}+x-30}\]
Split the second term in \(3{x}^{2}+x-30\) into two terms.
Multiply the coefficient of the first term by the constant term.
\[3\times -30=-90\]
Ask: Which two numbers add up to \(1\) and multiply to \(-90\)?
Split \(x\) as the sum of \(10x\) and \(-9x\).
\[3{x}^{2}+10x-9x-30\]
\[l\imath mx->3\times \frac{(2x+5)(x-3)}{3{x}^{2}+10x-9x-30}\]
Factor out common terms in the first two terms, then in the last two terms.
\[l\imath mx->3\times \frac{(2x+5)(x-3)}{x(3x+10)-3(3x+10)}\]
Factor out the common term \(3x+10\).
\[l\imath mx->3\times \frac{(2x+5)(x-3)}{(3x+10)(x-3)}\]
Cancel \(x-3\).
\[l\imath mx->3\times \frac{2x+5}{3x+10}\]
Simplify \(3\times \frac{2x+5}{3x+10}\) to \(\frac{3(2x+5)}{3x+10}\).
\[l\imath mx->\frac{3(2x+5)}{3x+10}\]
Regroup terms.
\[-+l\imath mx>\frac{3(2x+5)}{3x+10}\]
Divide both sides by \(\imath \).
\[-+lmx>\frac{\frac{3(2x+5)}{3x+10}}{\imath }\]
Simplify \(\frac{\frac{3(2x+5)}{3x+10}}{\imath }\) to \(\frac{3(2x+5)}{\imath (3x+10)}\).
\[-+lmx>\frac{3(2x+5)}{\imath (3x+10)}\]
Divide both sides by \(m\).
\[-+lx>\frac{\frac{3(2x+5)}{\imath (3x+10)}}{m}\]
Simplify \(\frac{\frac{3(2x+5)}{\imath (3x+10)}}{m}\) to \(\frac{3(2x+5)}{\imath m(3x+10)}\).
\[-+lx>\frac{3(2x+5)}{\imath m(3x+10)}\]
Divide both sides by \(x\).
\[-+l>\frac{\frac{3(2x+5)}{\imath m(3x+10)}}{x}\]
Simplify \(\frac{\frac{3(2x+5)}{\imath m(3x+10)}}{x}\) to \(\frac{3(2x+5)}{\imath mx(3x+10)}\).
\[-+l>\frac{3(2x+5)}{\imath mx(3x+10)}\]
Multiply both sides by \(-1\).
\[l<-\frac{3(2x+5)}{\imath mx(3x+10)}\]
l<-(3*(2*x+5))/(IM*m*x*(3*x+10))
