How do you simplify $(3x^2-5x-2)/(6x^3+2x^2+3x+1)$ ?

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Answer 1 · 2015-06-03T07:45:04

$color(red)((3x^2-5x-2))/color(purple)((6x^3+2x^2+3x+1))$

Factorising the numerator :
By splitting the middle term
$color(red)(3x^2-5x-2$

$3x^2-5x-2 = 3x^2-6x + 1x -2$
$= 3x(x-2)+1(x-2)$
$= color(red)((3x+1)(x-2)$

$= (6x^3+2x^2)+(3x+1)$
$= 2x^2(3x +1)+1(3x+1)$
$= color(purple)((2x^2+1) (3x +1)$

The expression becomes:
$= color(red)(cancel(3x+1)(x-2))/ color(purple)((2x^2+1) cancel(3x +1)$
$= color(red)((x-2))/ color(purple)((2x^2+1)$

How do you simplify (3x^2-5x-2)/(6x^3+2x^2+3x+1)(3x^2-5x-2)/(6x^3+2x^2+3x+1)?