How do you multiply #\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

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

#12x^2 - x - 6 = 12x^2 - 9x + 8x - 6 = 3x(4x - 3) + 2 (4x - 3)#

#=> (3x+2) (4x-3)#

#x^2 + 7x = 6 = x^2 + 6x + x + 6 = (x + 6) (x+1)#

#4x^2 - 27x + 18 = 4x^2 - 24x - 3x + 18 = (x-6) (4x-3)#

#((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)#