SOLUTION: 1) (2x+12)/(3x-15)/(2x^(2)-6x-20)/(x^(2)-10x+25) 2) (3x)/(x^2+3x-10)-(2x)/(x^2+x-6) 3) (2x-10)/(2x^2-5x-3)+(1)/(x-3)=3/(x-3)

Algebra ->  Rational-functions -> SOLUTION: 1) (2x+12)/(3x-15)/(2x^(2)-6x-20)/(x^(2)-10x+25) 2) (3x)/(x^2+3x-10)-(2x)/(x^2+x-6) 3) (2x-10)/(2x^2-5x-3)+(1)/(x-3)=3/(x-3)      Log On


   

Question 734748: 1) (2x+12)/(3x-15)/(2x^(2)-6x-20)/(x^(2)-10x+25)

2) (3x)/(x^2+3x-10)-(2x)/(x^2+x-6)

3) (2x-10)/(2x^2-5x-3)+(1)/(x-3)=3/(x-3)
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
       %28%282x%2B12%29%2F%283x-15%29%29%2F%28%282x%5E2-6x-20%29%2F%28x%5E2-10x%2B25%29%29

Write as a division of fractions:

       %282x%2B12%29%2F%283x-15%29%22%F7%22%282x%5E2-6x-20%29%2F%28x%5E2-10x%2B25%29

2x+12 factors as 2(x+6)
3x-15 factors as 3(x-5)
2x²-6x-20 factors as 2(x²-3x-10) or as 2(x-5)(x+2)
x²-10x+25 factors as (x-5)(x-5)

       %282%28x%2B6%29%29%2F%283%28x-5%29%29%22%F7%22%282%28x-5%29%28x%2B2%29%29%2F%28%28x-5%29%28x-5%29%29
 
Invert the second franction and change division to multiplication

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Cancel the 2's

       %28cross%282%29%28x%2B6%29%29%2F%283%28x-5%29%29%22%22%2A%22%22%28%28x-5%29%28x-5%29%29%2F%28cross%282%29%28x-5%29%28x%2B2%29%29

       %28%28x%2B6%29%29%2F%283%28x-5%29%29%22%22%2A%22%22%28%28x-5%29%28x-5%29%29%2F%28%28x-5%29%28x%2B2%29%29

Cancel one pair of (x-5)'s

       %28%28x%2B6%29%29%2F%283%28cross%28x-5%29%29%29%22%22%2A%22%22%28%28cross%28x-5%29%29%28x-5%29%29%2F%28%28x-5%29%28x%2B2%29%29

       %28x%2B6%29%2F3%22%22%2A%22%22%28x-5%29%2F%28%28x-5%29%28x%2B2%29%29

Cancel the other pair of (x-5)'s

       %28x%2B6%29%2F3%22%22%2A%22%22%28cross%28x-5%29%29%2F%28%28cross%28x-5%29%29%28x%2B2%29%29

       %28x%2B6%29%2F%283%28x%2B2%29%29

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

         %283x%29%2F%28x%5E2%2B3x-10%29%22%22-%22%22%282x%29%2F%28x%5E2%2Bx-6%29
          
         %283x%29%2F%28x%2B5%29%28x-2%29%29%22%22-%22%22%282x%29%2F%28%28x%2B3%29%28x-2%29%29 

Get LCD of (x+5)(x-2)(x+3)

         %283x%28x%2B3%29%29%2F%28x%2B5%29%28x-2%29%28x%2B3%29%29%22%22-%22%22%282x%28x%2B5%29%29%2F%28%28x%2B3%29%28x-2%29%28x%2B5%29%29

         %283x%5E2%2B9x%29%2F%28x%2B5%29%28x-2%29%28x%2B3%29%29%22%22-%22%22%282x%5E2%2B10x%29%2F%28%28x%2B3%29%28x-2%29%28x%2B5%29%29

The denominators are equal, so we combine the numerators over the LCD

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         %283x%5E2%2B9x-2x%5E2-10x%29%2F%28%28x%2B5%29%28x-2%29%28x%2B3%29%29

         %28x%5E2-x%29%2F%28%28x%2B5%29%28x-2%29%28x%2B3%29%29

         %28x%28x-1%29%29%2F%28%28x%2B5%29%28x-2%29%28x%2B3%29%29

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

          %282x-10%29%2F%282x%5E2-5x-3%29%22%22%2B%22%221%2F%28x-3%29%22%22=%22%223%2F%28x-3%29

          %282x-10%29%2F%28%28x-3%29%282x%2B1%29%29%22%22%2B%22%221%2F%28x-3%29%22%22=%22%223%2F%28x-3%29

Multiply through by the LCD of (x-3)(2x+1)  

          2x-10 + 1(2x+1) = 3(2x+1)
         2x - 10 + 2x + 1 = 6x + 3
                   4x - 9 = 6x + 3
                      -2x = 12
                        x = -6                        


Edwin