help simplify #2? i meant the first time (x^2+2x) is on the top?

Question

x^2+2x
=====
x^2+x-2

Answer 1

x^2+2x=x(x+2)

bottom has 2 roots:

x=(-1 +/ sqrt(1+4*2) ) / 2
i.e. x=-2 and x=1

so bottom is (x+2)(x-1)

and fraction reduces to:

x/(x-1)

Answer 2

first simplify each part:

x^2 + 2x = x(x+2)
x^2 + x - 2 = x^2 + 2x - x - 2 = x(x+2) - (x+2) = (x+2)(x-1)

now put it altogether:

x(x+2)
over
(x+2)(x-1)

You can notice that (x+2) in both expressions cancel each other, which leaves you with
x
over
(x-1) as a result.

Note:
- In this case we cannot perform usual checkup of the solution.
- should this be an equation problem, some extended rules would apply (won't go any further here, just to bring it to your attention)

Answer 3

x ( x + 2 )
===========
( x + 2 ) ( x + 1 )

The ( x + 2 ) 's cancel out. So you are left with:

x
====
x + 1

Answer 4

x(x+2)÷(x+2)(x-1)

cancel the (x-2) in the top and the bottom
so you have x ÷ (x-1)

Answer 5

It cant't be simplified anymore than it already is