How do you combine #9/(x^2-2x+1)-(x-3)/(x^2-x)#?

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Answer 1 · 2016-08-10T20:14:06

#(- x^2+13x-1)/(x(x-1)(x-1))#

We are subtracting with algebraic fractions - factorise first

#9/(x^2-2x+1)-(x-3)/(x^2-x)#

=#9/((x-1)(x-1)) color(red)(xx x/x)-((x-3))/(x(x-1)) color(red)(xx((x-1))/((x-1))#

#(9x- (x-3)(x-1))/(x(x-1)(x-1))" common denominator"#

#(9x- (x^2-4x+1))/(x(x-1)(x-1))#

#(9x- x^2+4x-1)/(x(x-1)(x-1))#

#(- x^2+13x-1)/(x(x-1)(x-1))#