If I am dividing the following:

Question

x^2+3x over x^2+2x-3 by x over x+1.. i know to do the recip. of x over x+1 and get the foll.
x^2 + 3x over x^2 + 2x -3 times x+1 over x... now
(x^2+3x)(x+1) over
(x^2+2x-3)(x)
now
x(x+2)(x+1)
x(x+2)(x-1)
the x+2 over x+2 = 1
so wouldn't the value be 1?

Answer 1

x^2+3x over x^2+2x-3 by x over x+1
= (x^2+3x)/(x^2+2x-3)*(x)/(x+1)
= x(x+3)/[(x+3)(x-1)*x?(x+1)
= x/(x-1)*x/(x+1)
= x^2/(x^1 - 1)