How do you combine #(x^2) / (x+5) - (25 )/ (x+5)#?

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Answer 1 · 2015-05-19T18:23:47

When you have the sum/subtraction of fractions that share the same denominator, you simply add/subtract the numerators:

#(x^2-25)/(x+5)#

However, we can factorate #x^2-25# by equaling it to zero and finding its roots:

#x^2-25=0#
#x^2=25#
#x=sqrt(25)#
#x_1=5#, which is the same as the factor #(x-5)=0#
#x_2=-5#, which is the same as the factor #(x+5)=0#

Now, rewriting,

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

Your final answer, then, is #(x-5)#