Manipulating Rational Expressions

We want to simplify the given rational expression. To do so, we will factor the numerator and denominator as much as possible. Then, we will cancel out common factors, if possible.

\frac{x ^{2} ( x + 2 ) ( x - 4 )}{6 x ( x ^{2} + x - 2 0 )}

Factor the denominator

WriteSumWrite as a sum

\frac{x ^{2} ( x + 2 ) ( x - 4 )}{6 x ( x ^{2} - 4 x + 5 x - 2 0 )}

FactorOutFactor out

x & 5

\frac{x ^{2} ( x + 2 ) ( x - 4 )}{6 x ( x ( x - 4 ) + 5 ( x - 4 ) )}

FactorOutFactor out

(x - 4)

\frac{x ^{2} ( x + 2 ) ( x - 4 )}{6 x ( x - 4 ) ( x + 5 )}

SplitIntoFactorsSplit into factors

\frac{x \cdot x \cdot ( x + 2 ) ( x - 4 )}{6 \cdot x \cdot ( x - 4 ) ( x + 5 )}

CancelCommonFacCancel out common factors

\frac{x \cdot x \cdot ( x + 2 ) ( x - 4 )}{6 \cdot x \cdot ( x - 4 ) ( x + 5 )}

SimpQuotSimplify quotient

\frac{x ( x + 2 )}{6 ( x + 5 )}

Manipulating Rational Expressions 1.10 - Solution