What is (12+r-r^2)/(r^3+3r^2) ?

The solution to (12+r-r^2)/(r^3+3r^2) is -(r-4)/(r^2)

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simplify (12+r-r^2)/(r^3+3r^2)

simplify

\frac{12 + r - r ^{2}}{r ^{3} + 3 r ^{2}}

- \frac{r - 4}{r ^{2}}

Solution steps

\frac{12 + r - r ^{2}}{r ^{3} + 3 r ^{2}}

Factor

12 + r - r^{2} : - (r + 3) (r - 4)

= \frac{- ( r + 3 ) ( r - 4 )}{r ^{3} + 3 r ^{2}}

Factor

r^{3} + 3 r^{2} : r^{2} (r + 3)

= \frac{- ( r + 3 ) ( r - 4 )}{r ^{2} ( r + 3 )}

Cancel the common factor:

r + 3

= \frac{- ( r - 4 )}{r ^{2}}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{r - 4}{r ^{2}}

\frac{5}{6 x ^{8}} - \frac{1}{7 x ^{5}}

\frac{1}{2} + \frac{1}{3} + \frac{1}{8}

\frac{( 3 x ^{\frac{3}{2}} y ^{3} )}{( x ^{2} y ^{- \frac{1}{2}} )}^{- 2}

2 \cdot 8

3 (3 x + 2) - 2 (3 x - 1)

What is (12+r-r^2)/(r^3+3r^2) ?
The solution to (12+r-r^2)/(r^3+3r^2) is -(r-4)/(r^2)