x^2-x-2/x+3 divided by 2x+6/17x+17?

Dividing by a fraction is same as inverting and multiplying the fraction.
=> (x^2 - x - 2)/x+3 * 17x + 17/2x + 6
Factorising,
=> (x^2 - x - 2)/ x + 3 * 17(x+1)/2(x+3)
=>17/2 * (x^2 - x - 2) (x+1)/ (x + 3)^2
=> 17/2 * (x^2 -2x + 1x - 2) * (x+1) / (x+3)^2
=> 17/2 * {x(x - 2) + (x -2) } * (x+1) / (x+3)^2
=> 17/2 * (x-2)(x+1) * (x+1) / (x+3)^2
=> 17/2 * (x-2)(x+1)^2 / (x+3)^2

notice that x^2 + 5x + 6 factorizes as (x + 2)(x + 3) so a uncomplicated denominator is that this expression putting the completed concern over this uncomplicated denominator :~ {2x(x + 3) = x(x + 2) -3} / (x + 2)(x + 3) i.e. (2x^2 + 6x = x^2 + 2x -3) / (x + 2)(x + 3) deducting x^2 + 2x -3 from 1st a million/2 of numerator provides x^2 + 4x + 3 = 0 Which factorizes as (x + 3)(x + a million) :: we've (x + 3)(x + a million) / (x + 2)(x + 3) ~ The (x + 3) cancels out leaving (x + a million) / (x + 2)

(x² - x - 2) (17x + 17)
------------------------------
(x + 3) (2x + 6)

(x - 2) (x + 1) (17) (x + 1)
-----------------------------
(2) (x + 3) (x + 3)

17 (x - 2) (x + 1) ²
------------------------
2 (x + 3) ²

(x^2 - x - 2)/(x + 3) ÷ (2x + 6)/(17x + 17)
= (x^2 + x - 2x - 2)/(x + 3) * [17(x + 1)]/[2(x + 3)]
= [(x + 1)(x - 2)]/(x + 3) * [17(x + 1)]/[2(x + 3)]
= [17(x + 1)^2(x - 2)]/[2(x + 3)^2]

(x^2-x-2/x+3)/(40x/17+17)

I just plugged in the equation to simplify and this is what I got. This site is really reliable but you might want to plug in the equation exactly how it is written into the site to be sure. Hope this helps.

Also http://www.quickmath.com/ has multiple functions for other math problems so the home site might be helpful for other homework problems as well.

The answer will be 17x^3-51x-34 divided by 2x^2+12x+18

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