Question 255303
OUr expression is:
{{{((x^2 - x) / (x^2 + 3x + 2)) / ((x^2 + 2x)/ (x^2 -1))}}}
step 1 - factor each part separately:
x^2-x = x(x-1)
x^2 + 3x + 2 = (x+2)(x+1)
x^2+ 2x = x(x+2)
x^2-1 = (x+1)(x-1)
we get
{{{(x*(x-1))/((x+2)(x+1))}}} / {{{(x*(x+2))/((x+1)(x-1))}}}
step 2-Multiply the top fraction by the reciprocal of the bottom fraction to get
{{{(x*(x-1))/((x+2)(x+1))}}} * {{{((x+1)(x-1))/(x*(x+2))}}}
step 3 - cancel where possible to get
{{{(x-1)^2 / (x+2)^2}}}