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

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) (Show Source): You can put this solution on YOUR website!
1) x squared-3x OVER 5x squared TIMES 10x OVER x squared-4x+3
*
:
* ; canceled 5x into 10x
:
(x-3) * ; canceled out x
:
; canceled out (x-3)
:
:
Solve.
2) 5 OVER x MINUS x-3 OVER x+2 = 22 OVER x squared + 2x
- =
:
- =
:
Multiply equation by x(x+2)
x(x+2)* - x(x+2)* = x(x+2)*
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.
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