Question #d7b37

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Question #d7b37

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Answer 1 · 2016-09-22T16:16:57

$\frac{x^{2} - 6}{12 x + 9}$ $(x^2-6)/(12x+9)$

Explanation:

Assumption: the given expression is meant to be:

$\frac{\frac{x}{3} - 2}{\frac{3}{x^{2}} + \frac{4}{x}}$ $(x/3 -2)/(3/x^2+4/x)$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$Consider the numerator$ $color(blue)("Consider the numerator")$

$\frac{x}{3} - 2 \to \frac{x}{3} - \frac{6}{3} = \frac{x - 6}{3}$ $x/3-2 -> x/3-6/3 color(blue)(= (x-6)/3)$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$Consider the denominator$ $color(blue)("Consider the denominator")$

$\frac{3}{x^{2}} + \frac{4}{x} \to \frac{3 x + 4 x^{2}}{x^{2}}$ $3/x^2+4/x -> (3x+4x^2)/x^2$
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$Putting it all together$ $color(blue)("Putting it all together")$

$\frac{x - 6}{3} \div \frac{3 x + 4 x^{2}}{x^{2}}$ $(x-6)/3 -: (3x+4x^2)/x^2$

$\frac{x - 6}{3} \times \frac{x^{2}}{3 x + 4 x^{2}} = \frac{x^{3} - 6 x^{2}}{12 x^{2} + 9 x}$ $(x-6)/3xxx^2/(3x+4x^2) " "=" "(x^3-6x^2)/(12x^2+9x)$

Factor out $x$ $x$ from top and bottom.

$(cancel(x)^1(x^2-6))/(cancel(x)^1(12x+9))$

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Question #d7b37

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