so remember how you can factor out ones
like (4/8)=(4/4)(1/2)=(1)(1/2)
so first factor each think see if we can simplify any of them
[tex] \frac{ \frac{(x+1)(x+1)}{(x-2)} }{ \frac{(x+1)(x-1)}{(x+2)(x-2)} } [/tex]
can't
ok so remember division of fractions
(a/b)/(c/d)=(a/b)(d/c)=(ad)/(bc)
invert and multiply
so
[tex] \frac{ \frac{(x+1)(x+1)}{(x-2)} }{ \frac{(x+1)(x-1)}{(x+2)(x-2)} } [/tex]=
[tex](\frac{(x+1)(x+1)}{(x-2)}) ( \frac{(x+2)(x-2)}{(x+1)(x-1)}}) [/tex]=
[tex]\frac{(x+1)(x+1)(x+2)(x-2)}{(x-2)(x+1)(x-1)}[/tex]=
[tex]( \frac{(x+1)(x+2)}{(x-1)} )( \frac{(x+1)(x-2)}{(x+1)(x-2)} )[/tex]=
[tex]( \frac{(x+1)(x+2)}{(x-1)} )( 1)[/tex]=
[tex]\frac{(x+1)(x+2)}{(x-1)} [/tex]=
[tex]\frac{x^2+3x+2}{x-1} [/tex]
