SOLUTION: Perform the operations and simplify. 2/(x^2 - 4x +3) + 3/(x^2 - 8x + 15) - 6/(x^2 - 6x + 5)

Algebra ->  Exponents -> SOLUTION: Perform the operations and simplify. 2/(x^2 - 4x +3) + 3/(x^2 - 8x + 15) - 6/(x^2 - 6x + 5)      Log On


   

Question 62272: Perform the operations and simplify. 2/(x^2 - 4x +3) + 3/(x^2 - 8x + 15) - 6/(x^2 - 6x + 5)
Answer by gsmani_iyer(201) About Me  (Show Source):
You can put this solution on YOUR website!

2%2F%28x%5E2-4x%2B3%29+%2B+3%2F%28x%5E2-8x%2B15%29+-+6%2F%28x%5E2-6x%2B5%29 Now let's factorise the denominators as under:
= 2%2F%28x-3%29%28x-1%29%2B3%2F%28x-5%29%28x-3%29-6%2F%28x-5%29%28x-1%29
Now, let's take the LCM of the denominators which comes to %28x-1%29%28x-3%29%28x-5%29and simplify the above expression as under:

= %282%28x-5%29%2B3%28x-1%29-6%28x-3%29%29%2F%28x-1%29%28x-3%29%28x-5%29. By expanding the numerator, we get

= %282x-10%2B3x-3-6x%2B18%29%2F%28x-1%29%28x-3%29%28x-5%29 = %28-x%2B5%29%2F%28x-1%29%28x-3%29%28x-5%29

= %28-1%28x-5%29%29%2F%28x-1%29%28x-3%29%28x-5%29 = %28-1%2Across%28%28x-5%29%29%29%2F%28x-1%29%28x-3%29cross%28%28x-5%29%29

= %28-1%29%2F%28x-1%29%28x-3%29. Answer. That's all. I hope this is clear to you. In case of any doubt, feel free to contact me. All the best.

gsm