Cancel \(d\).
\[\frac{a}{b}<cabc\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{a}{b}<{c}^{2}ab\]
Multiply both sides by \(b\).
\[a<{b}^{2}{c}^{2}a\]
Subtract \(a\) from both sides.
\[0<{b}^{2}{c}^{2}a-a\]
Factor out the common term \(a\).
\[0<a({b}^{2}{c}^{2}-1)\]
Rewrite \({b}^{2}{c}^{2}-1\) in the form \({a}^{2}-{b}^{2}\), where \(a=bc\) and \(b=1\).
\[0<a({(bc)}^{2}-{1}^{2})\]
Use Difference of Squares: \({a}^{2}-{b}^{2}=(a+b)(a-b)\).
\[0<a(bc+1)(bc-1)\]
Divide both sides by \(bc+1\).
\[0<a(bc-1)\]
Divide both sides by \(bc-1\).
\[0<a\]
Switch sides.
\[a>0\]
a>0
