How do you combine #2/(3x-15)+x/(25-x^2)#?

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Answer 1 · 2017-02-09T14:57:15

#2/(3x-15)+x/(25-x^2)=(10-x)/(3x^2-75)#

#2/(3x-15)+x/(25-x^2)#

= #2/(3(x-5))-x/(x^2-25)# - we have modified so that both may have common factor #(x-5)#

= #2/(3(x-5))-x/(x^2-5^2)#

= #2/(3(x-5))-x/((x-5)(x+5))#

= #(2(x+5)-3x)/(3(x-5)(x+5))#

= #(2x+10-3x)/(3(x-5)(x+5))#

= #(10-x)/(3(x-5)(x+5))#

= #(10-x)/(3(x^2-25))#

= #(10-x)/(3x^2-75)#