x^3-36x over x^2+7x+6, divided by 6x^2-x^3 over x^2+x
I know the right answer is -1, but I can't seem to get to it.
I've gotten as far as [x(x-6)]/1] * 1/[x^2(6-x)], which is then equal to [x(x-6)]/x^2(6-x). And then would I reduce the x and x^2 to 1 and x, making the equation [x-6] / [x(6-x]?
But now I'm stuck with that extra 'x' aren't I? Because x-6 over 6-x would reduce to -1, the answer. What about that x?
The expression can be written as
((x^2+x)*(x^3-36*x))/((x^2+7*x+6)*(6*x^2-x^3));
and it does simplify to -1.
The numerator can be factored into
x(x+1)x(x+6)(x-6)
and the denominator can be written as:
(x+1)(x+6)x²(6-x)
=-(x+1)(x+6)x²(x-6)
After cancelling factors, you'd end up with -1.