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Question

(2x)/(x+4)-(12)/(x-3)=(4x^2+36)/(x^2-9)? factorize...

Answer 1

(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.

Answer 2

The equation is

Irreducible factorization of

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Comments

The equation is .

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Factorization of is .