How do you divide $\frac{5}{3 n^{3} + 3 n^{2}} \div \frac{1}{3 n^{2}}$ $\frac { 5} { 3n ^ { 3} + 3n ^ { 2} } \div \frac { 1} { 3n ^ { 2} }$ ?

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How do you divide $\frac{5}{3 n^{3} + 3 n^{2}} \div \frac{1}{3 n^{2}}$ $\frac { 5} { 3n ^ { 3} + 3n ^ { 2} } \div \frac { 1} { 3n ^ { 2} }$ ?

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Answer 1 · 2017-04-20T01:24:57

$\frac{5}{3 n^{3} + 3 n^{2}} \div \frac{1}{3 n^{2}} = \frac{5}{n + 1}$ $frac{5}{3n^3+3n^2}divfrac{1}{3n^2}=frac{5}{n+1}$

Explanation:

$\frac{5}{3 n^{3} + 3 n^{2}} \div \frac{1}{3 n^{2}}$ $frac{5}{3n^3+3n^2}divfrac{1}{3n^2}$

Factor the denominator of the first fraction
$= \frac{5}{(3 n^{2}) (n + 1)} \div \frac{1}{3 n^{2}}$ $=frac{5}{(3n^2)(n+1)}div frac{1}{3n^2}$

Dividing is the same as multiplying by the reciprocal:
$= \frac{5}{(3 n^{2}) (n + 1)} \cdot (3 n^{2})$ $=frac{5}{color(red)((3n^2))(n+1)}*color(red)((3n^2))$

Cancel terms that are repeated on the numerator and denominator:
$= \frac{5}{n + 1}$ $=frac{5}{n+1}$

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How do you divide $\frac{5}{3 n^{3} + 3 n^{2}} \div \frac{1}{3 n^{2}}$ $\frac { 5} { 3n ^ { 3} + 3n ^ { 2} } \div \frac { 1} { 3n ^ { 2} }$ ?

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Explanation:

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How do you divide $\frac{5}{3 n^{3} + 3 n^{2}} \div \frac{1}{3 n^{2}}$ $\frac { 5} { 3n ^ { 3} + 3n ^ { 2} } \div \frac { 1} { 3n ^ { 2} }$ ?