How do you simplify #(x^2-9)/(x^2+2x-15)#?

1 Answer
Jim G.
Jun 16, 2017

#(x+3)/(x+5)#

Explanation:

#"factorise the numerator/denominator and cancel any"#
#color(blue)"common factors"#

#"the numerator is a "color(blue)"dufference of squares"#

#rArrx^2-9=(x-3)(x+3)#

#"the denominator can be factorised by 'splitting' the x-term"#

#x^2-3x+5x-15larr -3x+5x=2x#

#=color(red)(x)(x-3)color(red)(+5)(x-3)#

#=(x-3)(color(red)(x+5))#

#rArr(x^2-9)/(x^2+2x-15)#

#=(cancel((x-3))(x+3))/(cancel((x-3))(x+5))#

#=(x+3)/(x+5)to(x!=-5)#

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