Question 256883
1. (2x^2 + x - 3)/9 times (x + 1)^2/(2x^2 + 5x + 3) 
step 1 - factor all possible polynomials as
{{{(2x + 3)(x-1)/9}}} * {{{(x + 1)^2/((2x+3)(x+1))}}} 
step 2 - cancel where needed as
{{{((x-1)/9)*(x+1)}}}
which is simplified as
{{{(x^2-1)/9}}}
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2. 1/(25 - y^2) divided by (6 - 3y)/y^2 - 7y + 10) 
step 1 - factor all possible polynomials as
{{{1/(5+y)(5-y))}}} /  {{{(3(2-y))/((y-5)(y+3)) }}}
step 2 - multiply by reciprocal to get
{{{1/(5+y)(5-y))}}} * {{{((y-5)(y+3))/(3(2-y))}}
step 3 - cancel where needed as
{{{-1/(y+5)}}} * {{{(y+3)/(3*(2-y))}}}
{{{-(y+3)/(-3y^2-3y+10)}}}
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3. abc/(a^2 - 3a - 10) divided by a^2/(a^2 - 25) times (4 - a^2/9b^2 - 4 divided by (abc + 5bc)/(3ab - 2a) 
step 1 - factor all possible polynomials
{{{abc/((a-5)(a+2))}}} / {{{a^2/((a+5)(a-5))}}} * {{{(2+a)(2-a)/((3b+2)(3b-2))}}} / {{{bc(a+5)/(3b-2a)}}}
which becomes
{{{abc/((a-5)(a+2))}}} * {{{((a+5)(a-5))/a^2}}} * {{{(3b-2a)/bc(a+5)}}} * {{{(2+a)(2-a)/((3b+2)(3b-2))}}}
step 2 - reduce as needed to get
{{{(a+5)(2-a)(3b-2a)}}} / {{{a(3b+2)(3b-2)}}}
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4. (n^2 + 5n + 6)/(n^2 + 7n + 12 times (n^2 + 9n + 20/(n^2 + 11n + 30)
step 1  -factor all possible polynomials to get
{{{((n+3)(n+2))/((n+3)(n+4))}}} * {{{((n+4)(n+5))/((n+5)(n+6))}}}
this reduces nicely to
{{{(n+2)/(n+6)}}}