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

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

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

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

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

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

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

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