How do you combine #(2x)/(x-3) - (3x)/(x-5)#?

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Answer 1 · 2015-05-24T11:27:25

As with adding or subtracting numerical fractions, the first step is to form a common denominator (bottom)...

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

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

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

#= (2x^2-10x-3x^2+9x)/((x-3)(x-5))#

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

#=-(x(x+1))/((x-3)(x-5))#

or if you prefer

#=-(x^2+x)/(x^2-8x+15)#