SOLUTION: Subtract {{{(1)/(x^2-2x)-5/(x^2-4x+4)}}}

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Subtract {{{(1)/(x^2-2x)-5/(x^2-4x+4)}}}       Log On


   

Question 153924: Subtract

%281%29%2F%28x%5E2-2x%29-5%2F%28x%5E2-4x%2B4%29
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%281%29%2F%28x%5E2-2x%29-5%2F%28x%5E2-4x%2B4%29 Start with the given expression


%281%29%2F%28x%28x-2%29%29-5%2F%28x%5E2-4x%2B4%29 Factor x%5E2-2x to get x%28x-2%29


%281%29%2F%28x%28x-2%29%29-5%2F%28%28x-2%29%28x-2%29%29 Factor x%5E2-4x%2B4 to get %28x-2%29%28x-2%29


Notice how the LCD is x%28x-2%29%28x-2%29


%28%28x-2%29%2F%28x-2%29%29%28%281%29%2F%28x%28x-2%29%29%29-5%2F%28%28x-2%29%28x-2%29%29 Multiply the first fraction by %28x-2%29%2F%28x-2%29


%28x-2%29%2F%28x%28x-2%29%28x-2%29%29-5%2F%28%28x-2%29%28x-2%29%29 Combine and multiply the fractions


%28x-2%29%2F%28x%28x-2%29%28x-2%29%29-%28x%2Fx%29%285%2F%28%28x-2%29%28x-2%29%29%29 Multiply the second fraction by %28x%29%2F%28x%29


%28x-2%29%2F%28x%28x-2%29%28x-2%29%29-%285x%29%2F%28x%28x-2%29%28x-2%29%29 Combine and multiply the fractions



Since the denominators are now equal, this means that we can subtract the fractions. To do this, simply subtract the numerators and place that over the common denominator.


%28x-2-5x%29%2F%28x%28x-2%29%28x-2%29%29


%28-6x-2%29%2F%28x%28x-2%29%28x-2%29%29 Combine like terms.



-------------------------------------------

Answer:

So %281%29%2F%28x%5E2-2x%29-%285%29%2F%28x%5E2-4x%2B4%29 subtracts and simplifies to %28-6x-2%29%2F%28x%28x-2%29%28x-2%29%29