SOLUTION: can you help me please by subtracting this rational expression (x)/(x^2 - 5x + 6)- (3)/(3-x)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: can you help me please by subtracting this rational expression (x)/(x^2 - 5x + 6)- (3)/(3-x)      Log On


   

Question 630792: can you help me please by subtracting this rational expression
(x)/(x^2 - 5x + 6)- (3)/(3-x)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
can you help me please by subtracting this rational expression
%28x%29%2F%28x%5E2+-+5x+%2B+6%29 - %283%29%2F%283-x%29
;
Factor the 1st denominator
%28x%29%2F%28%28x-2%29%28x-3%29%29 - %283%29%2F%283-x%29
;
Convert the 2nd denominator, factor out -1
%28x%29%2F%28%28x-2%29%28x-3%29%29 - %283%29%2F%28-1%28x-3%29%29
:
the minus one changes the sign
%28x%29%2F%28%28x-2%29%28x-3%29%29 + %283%29%2F%28%28x-3%29%29
;
The common denominator is (x-2)(x-3)
%28x+%2B+3%28x-2%29%29%2F%28%28x-2%29%28x-3%29%29 = %28x%2B3x-6%29%2F%28%28x-2%29%28x-3%29%29 = %284x-6%29%2F%28%28x-2%29%28x-3%29%29
Or you can Factor out 2
%282%282x-3%29%29%2F%28%28x-2%29%28x-3%29%29
:
Did all this make sense to you?