How do you simplify #x/(x^2-16) + (x-2)/(x^2-5x+4)#?

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Answer 1 · 2018-06-15T08:02:07

#(2x^2+x-8)/((x-4)(x+4)(x-1))#

Note that

#x^2-16=(x-4)(x+4)#

#x^2-5x+4=(x-4)(x-1)#
so we have to add

#(x(x-1))/((x-4)(x+4)(x-1))#

#((x-2)(x+4))/((x-4)(x-1)(x+4))#
and we have

#x(x-1)=x^2-x#

#(x-2)(x+4)=x^2+2x-8#
so we get the result above.