How do I simplify $\frac{2 x}{x + 5} \div \frac{6 x^{2}}{2 x + 10}$ $(2x)/(x+5)÷(6x^2)/(2x+10)$ ?

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How do I simplify $\frac{2 x}{x + 5} \div \frac{6 x^{2}}{2 x + 10}$ $(2x)/(x+5)÷(6x^2)/(2x+10)$ ?

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Answer 1 · 2015-08-09T02:23:00

I found: $\frac{2}{3 x}$ $2/(3x)$

Explanation:

You can write it (changing the division into a multiplication) as:
$\frac{2 x}{x + 5} \times \frac{2 x + 10}{6 x^{2}} =$ $(2x)/(x+5)xx(2x+10)/(6x^2)=$
and rearranging:
$= \frac{2 x}{6 x^{2}} \times \frac{2 (x + 5)}{x + 5} =$ $=(2x)/(6x^2)xx(2(x+5))/(x+5)=$
$=(cancel(2)cancel(x))/(cancel(6)^3x^cancel(2))xx(2cancel((x+5)))/cancel((x+5))=$
Finally:
$=2/(3x)$

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How do I simplify $\frac{2 x}{x + 5} \div \frac{6 x^{2}}{2 x + 10}$ $(2x)/(x+5)÷(6x^2)/(2x+10)$ ?

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How do I simplify $\frac{2 x}{x + 5} \div \frac{6 x^{2}}{2 x + 10}$ $(2x)/(x+5)÷(6x^2)/(2x+10)$ ?