How do you simplify #(x^2-9)/(x^2-16)*(x^2-8x+16)/(x^2+6x+9)#?
2 Answers
Factor and cancel out common factors to find:
with exclusion
Explanation:
Use difference of squares identity:
Use perfect square trinomial identity:
with exclusion
Explanation:
Ideas:
-
# (x + y)^2 = x^2 + 2xy + y^2 #
Thus, in the numerator in the fraction on the right, put#y=4# and in the denominator, put#y=3# . -
# x^2 - y^2 = (x + y) (x - y) #
Again, like in the previous point, in the numerator in the fraction on the left, put#y=3# and in the denominator, put#y=4# . -
In the 3rd step, cancel out common terms, namely
#(x-4)# and#(x+3)# .