How do you multiply $\frac{12 x^{2} - x - 6}{x^{2} - 1} \cdot \frac{x^{2} + 7 x + 6}{4 x^{2} - 27 x + 18}$ $\frac{12x^2-x-6}{x^2-1} \cdot \frac{x^2+7x+6}{4x^2-27x+18}$ ?

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How do you multiply $\frac{12 x^{2} - x - 6}{x^{2} - 1} \cdot \frac{x^{2} + 7 x + 6}{4 x^{2} - 27 x + 18}$ $\frac{12x^2-x-6}{x^2-1} \cdot \frac{x^2+7x+6}{4x^2-27x+18}$ ?

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Answer 1 · 2018-08-04T06:41:06

$\Rightarrow \frac{(3 x + 2) (x + 6)}{(x - 1) (x - 6)} = \frac{3 x^{2} + 20 x + 12}{x^{2} - 7 x + 6}$ $color(indigo)(=> ((3x+2)(x+6)) / ((x-1)(x-6)) = (3x^2 + 20x + 12) / (x^2 - 7x + 6)$

Explanation:

$12 x^{2} - x - 6 = 12 x^{2} - 9 x + 8 x - 6 = 3 x (4 x - 3) + 2 (4 x - 3)$ $12x^2 - x - 6 = 12x^2 - 9x + 8x - 6 = 3x(4x - 3) + 2 (4x - 3)$

$\Rightarrow (3 x + 2) (4 x - 3)$ $=> (3x+2) (4x-3)$

$x^{2} + 7 x = 6 = x^{2} + 6 x + x + 6 = (x + 6) (x + 1)$ $x^2 + 7x = 6 = x^2 + 6x + x + 6 = (x + 6) (x+1)$

$4 x^{2} - 27 x + 18 = 4 x^{2} - 24 x - 3 x + 18 = (x - 6) (4 x - 3)$ $4x^2 - 27x + 18 = 4x^2 - 24x - 3x + 18 = (x-6) (4x-3)$

$(\frac{12 x^{2} - x - 6}{x^{2} - 1}) \cdot (\frac{x^{2} + 7 x + 6}{4 x^{2} - 27 x + 18})$ $((12x^2 - x - 6)/(x^2-1)) * ((x^2 + 7x + 6) / (4x^2 - 27x + 18))$

$=> ((3x+2)cancel((4x-3)))/(cancel((x+1))(x-1)) * ((x+6)cancel((x+1)))/((x-6)cancel((4x-3)))$

$color(indigo)(=> ((3x+2)(x+6)) / ((x-1)(x-6)) = (3x^2 + 20x + 12) / (x^2 - 7x + 6)$

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How do you multiply $\frac{12 x^{2} - x - 6}{x^{2} - 1} \cdot \frac{x^{2} + 7 x + 6}{4 x^{2} - 27 x + 18}$ $\frac{12x^2-x-6}{x^2-1} \cdot \frac{x^2+7x+6}{4x^2-27x+18}$ ?

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How do you multiply $\frac{12 x^{2} - x - 6}{x^{2} - 1} \cdot \frac{x^{2} + 7 x + 6}{4 x^{2} - 27 x + 18}$ $\frac{12x^2-x-6}{x^2-1} \cdot \frac{x^2+7x+6}{4x^2-27x+18}$ ?