How do you simplify #((3x-1) / (x^2+5x)) - ((2x-1) / (x^2-25))#?

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Answer 1 · 2018-06-09T08:23:35

#(x^2-15x+5)/(x(x+5)(x-5))#

#(3x-1)/(x^2+5x)-(2x-1)/(x^2-25)#

Factorise your denominator
=#(3x-1)/(x(x+5))-(2x-1)/((x-5)(x+5))#

Now you want to make your denominator the same
=#((3x-1)(x-5)-(2x-1)(x))/(x(x+5)(x-5))#

Expand your brackets
=#(3x^2-16x+5-2x^2+x)/(x(x+5)(x-5))#

Simplify
=#(x^2-15x+5)/(x(x+5)(x-5))#

Answer 2 · 2018-06-09T08:33:12

#(x^2-15x+5)/((x(x+5)(x-5))#

Writing
#(3x-1)/(x(x+5))-(2x-1)/((x-5)(x+5))#
as

#((3x-1)(x-5))/(x(x+5)(x-5))-(x(2x-1))/((x(x-5)(x+5))#
this is equal to

#(3x^2-x-15x+5-(2x^2-x))/(x(x-5)(x+5))#
collecting likewise terms

#(x^2-15x+5)/(x(x+5)(x-5))#