Question 5072
{{{(x^2-8x+7)/ (x^2+3x-4) *  (x^2+3x-10)/ (x^2-9x+14) }}}


The critical step here is to FACTOR, FACTOR, FACTOR, and FACTOR!!

You are NOT allowed to divide out terms such as {{{x^2}}} or numbers that are involved in addition or subtractions.  Everything must be in FACTORED form in order to reduce the fractions.


{{{(x-7)(x-1)/ (x+4)(x-1) *  (x+5)(x-2)/ (x-7)(x-2) }}}


Now you can divide out the factors that are the same.  You can divide out ANY factor of ANY numerator with ANY factor of ANY denominator.  This is a good place for a "cartoon" by tutor and owner of this website Igor Chudov, but I haven't learned to do that yet.  Maybe he will add a cartoon to this solution to show how the factors divide out.  Until then, just divide out the factors of (x-7), (x-1), and (x-2).  What is left is the (x+5) in the numerator, and the (x+4) in the denominator.


Final answer:  {{{ (x+5) /(x+4) }}}


R^2 at SCC