How to simplify this .?

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How to simplify this .?

$\frac{4 x^{2} - y^{2}}{12 x^{2} - 4 x y - y^{2}}$ $(4x^2 - y^2)/(12x^2 - 4xy-y^2)$

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Answer 1 · 2017-07-31T18:13:50

$\frac{4 x^{2} - y^{2}}{12 x^{2} - 4 x y - y^{2}} = \frac{2 x + y}{6 x + y}$ $(4x^2-y^2)/(12x^2-4xy-y^2) = (2x+y)/(6x+y)$

with exclusion $2 x \neq y$ $2x != y$

Explanation:

Given:

$\frac{4 x^{2} - y^{2}}{12 x^{2} - 4 x y - y^{2}}$ $(4x^2-y^2)/(12x^2-4xy-y^2)$

We can factor both numerator and denominator and then cancel any common factor.

The numerator is a difference of squares, so factors as:

$4 x^{2} - y^{2} = {(2 x)}^{2} - y^{2} = (2 x - y) (2 x + y)$ $4x^2-y^2 = (2x)^2-y^2 = (2x-y)(2x+y)$

To factor the denominator find a pair of factors of $12$ $12$ which differ by $4$ $4$ . The pair $6, 2$ $6, 2$ works, so use that to split the middle term and factor by grouping:

$12 x^{2} - 4 x y - y^{2} = (12 x^{2} - 6 x y) + (2 x y - y^{2})$ $12x^2-4xy-y^2 = (12x^2-6xy)+(2xy-y^2)$

$12 x^{2} - 4 x y - y^{2} = 6 x (2 x - y) + y (2 x - y)$ $color(white)(12x^2-4xy-y^2) = 6x(2x-y)+y(2x-y)$

$12 x^{2} - 4 x y - y^{2} = (6 x + y) (2 x - y)$ $color(white)(12x^2-4xy-y^2) = (6x+y)(2x-y)$

So we find:

$(4x^2-y^2)/(12x^2-4xy-y^2) = (color(red)(cancel(color(black)((2x-y))))(2x+y))/((6x+y)color(red)(cancel(color(black)((2x-y)))))$

$color(white)((4x^2-y^2)/(12x^2-4xy-y^2)) = (2x+y)/(6x+y)$

with exclusion $2x != y$

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How to simplify this .?

$\frac{4 x^{2} - y^{2}}{12 x^{2} - 4 x y - y^{2}}$ $(4x^2 - y^2)/(12x^2 - 4xy-y^2)$

1 Answer

Explanation:

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Science

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Humanities

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How to simplify this .?

(4x^2 - y^2)/(12x^2 - 4xy-y^2)4x2−y212x2−4xy−y2(4x^2 - y^2)/(12x^2 - 4xy-y^2)

1 Answer

Explanation:

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$\frac{4 x^{2} - y^{2}}{12 x^{2} - 4 x y - y^{2}}$ $(4x^2 - y^2)/(12x^2 - 4xy-y^2)$