What is ((8k+12)/9)/(k/3+1/2) ?

The solution to ((8k+12)/9)/(k/3+1/2) is 8/3

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simplify ((8k+12)/9)/(k/3+1/2)

simplify

\frac{\frac{8 k + 12}{9}}{\frac{k}{3} + \frac{1}{2}}

\frac{8}{3}

Solution steps

\frac{\frac{8 k + 12}{9}}{\frac{k}{3} + \frac{1}{2}}

Apply the fraction rule:

\frac{\frac{a}{b}}{c} = \frac{a}{b \cdot c}

= \frac{8 k + 12}{9 ( \frac{k}{3} + \frac{1}{2} )}

Simplify

9 (\frac{k}{3} + \frac{1}{2}) : \frac{3 ( 2 k + 3 )}{2}

= \frac{8 k + 12}{\frac{3 ( 2 k + 3 )}{2}}

Apply the fraction rule:

\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b}

= \frac{( 8 k + 12 ) \cdot 2}{3 ( 2 k + 3 )}

Cancel

\frac{( 8 k + 12 ) \cdot 2}{3 ( 2 k + 3 )} : \frac{8}{3}

= \frac{8}{3}

\frac{p}{3} = 2

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