How do you simplify #(x^2-4)/(x^2-7x+10) div (x^2+6x+5)/(x^2-25)#?

1 Answer
Mar 28, 2018

Answer:

#(x+2)/(x+1)#

Explanation:

Rewrite
#(x^2-4)/(x^2-7+10)/(x^2+6x+5)/(x^2-25)#

Factor everything out
#((x+2)(x-2))/((x-5)(x-2))/((x+1)(x+5))/((x+5)(x-5))#

Cancel like terms
#(x+2)/(x-5)/(x+1)/(x-5)#

Dividing by a fraction is the same as multiplying buy the repciprocal
#(x+2)/(x-5)*(x-5)/(x+1)#

Cancel like terms
#(x+2)/1*1/(x+1)#

Multiply
#(x+2)/(x+1)#