SOLUTION: Can you PLEASE help me out with a few problems? I can not figure them out to save my life. Thank you in advance!! Solve. 1) x squared-3x OVER 5x squared TIMES 10x OVER x square

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can you PLEASE help me out with a few problems? I can not figure them out to save my life. Thank you in advance!! Solve. 1) x squared-3x OVER 5x squared TIMES 10x OVER x square      Log On


   

Question 125759: Can you PLEASE help me out with a few problems? I can not figure them out to save my life. Thank you in advance!!
Solve.
1) x squared-3x OVER 5x squared TIMES 10x OVER x squared-4x+3
Solve.
2) 5 OVER x MINUS x-3 OVER x+2 = 22 OVER x squared +2x
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
1) x squared-3x OVER 5x squared TIMES 10x OVER x squared-4x+3
%28%28x%5E2-3x%29%29%2F%28%285x%5E2%29%29 * %28%2810x%29%29%2F%28%28x%5E2-4x%2B3%29%29
:
%28x%28x-3%29%29%2F%28%28x%29%29 * %28%282%29%29%2F%28%28x-3%29%28x-1%29%29; canceled 5x into 10x
:
(x-3) * %28%282%29%29%2F%28%28x-3%29%28x-1%29%29; canceled out x
:
%28%282%29%29%2F%28%28x-1%29%29; canceled out (x-3)
:
:
Solve.
2) 5 OVER x MINUS x-3 OVER x+2 = 22 OVER x squared + 2x
5%2Fx - %28%28x-3%29%29%2F%28%28x%2B2%29%29 = 22%2F%28%28x%5E2%2B2x%29%29
:
5%2Fx - %28%28x-3%29%29%2F%28%28x%2B2%29%29 = 22%2F%28x%28x%2B2%29%29
:
Multiply equation by x(x+2)
x(x+2)*5%2Fx - x(x+2)*%28%28x-3%29%29%2F%28%28x%2B2%29%29 = x(x+2)*22%2F%28x%28x%2B2%29%29
Cancel out the denominators and you have:
:
5(x+2) - x(x-3) = 22
:
5x + 10 - x^2 + 3x = 22; multiplied what's inside the brackets
:
5x + 3x - x^2 + 10 - 22 = 0
:
-x^2 + 8x - 12 = 0
:
This is easier to factor if we change the signs, multiiply by -1
x^2 - 8x + 12 = 0
factors to:
(x-6)(x-2) = 0
x = +6
x = +2
:
:
You can check both solutions in the original equation to confirm they are correct.