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
\(\frac{ \frac{(x+1)(x+1)}{(x-2)} }{ \frac{(x+1)(x-1)}{(x+2)(x-2)} }\)
can't
ok so remember division of fractions
(a/b)/(c/d)=(a/b)(d/c)=(ad)/(bc)
invert and multiply
so
\(\frac{ \frac{(x+1)(x+1)}{(x-2)} }{ \frac{(x+1)(x-1)}{(x+2)(x-2)} }\)=
\((\frac{(x+1)(x+1)}{(x-2)}) ( \frac{(x+2)(x-2)}{(x+1)(x-1)}})\)=
\(\frac{(x+1)(x+1)(x+2)(x-2)}{(x-2)(x+1)(x-1)}\)=
\(( \frac{(x+1)(x+2)}{(x-1)} )( \frac{(x+1)(x-2)}{(x+1)(x-2)} )\)=
\(( \frac{(x+1)(x+2)}{(x-1)} )( 1)\)=
\(\frac{(x+1)(x+2)}{(x-1)}\)=
\(\frac{x^2+3x+2}{x-1}\)
