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(2x)/(x+4)-(12)/(x-3)=(4x^2+36)/(x^2-9)? factorize...
asked Apr 5, 2013 in ALGEBRA 2 by angel12 Scholar

2 Answers

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(2x) / (x + 4) - (12) / (x - 3) = (4x2 + 36) / (x2 - 9)

2x(x - 3) - 12(x + 4) / (x + 4)(x - 3) = (4x2 + 36) / (x - 3)(x + 3)

Cancel the common term x - 3 to each side

2x(x - 3) - 12(x + 4) / (x + 4) = (4x2 + 36) / (x + 3)

Divided each side by 2

[x(x - 3) - 6(x + 4)] / x + 4 = (2x2 + 18) / (x + 3)

(x2 - 3x -6x - 24) / x + 4 = (2x2 + 18) / (x + 3)

(x2 - 9x -24) / x + 4 = (2x2 + 18) / x + 3

Multiply each side by ( x + 3)(x + 4)

(x2 - 9x -24)(x + 3) = (2x2 + 18)(x + 4)

x3 -9x2 -24x +3x2 -27x -72 = 2x3 + 18x + 8x2 + 72

Simplify

x2 - 6x2 - 51x - 72 = 2x3 + 8x2 +18x +72

x3 + 14x2 + 69x +144 = 0

This is a cubic equation . It have three roots. It have no factors.

answered Apr 6, 2013 by diane Scholar
edited Apr 6, 2013 by diane
0 votes

The equation is image

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Irreducible factorization of image

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answered Jul 4, 2014 by david Expert
edited Jul 4, 2014 by david

The equation is image.

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Factorization of image is image.

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