SOLUTION: How do you solve a rational expression: 7x+3/x2 - 8X+15 +3x/x-5= 1/3-x

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Question 1063242: How do you solve a rational expression:
7x+3/x2 - 8X+15 +3x/x-5= 1/3-x
Found 3 solutions by stanbon, MathTherapy, ikleyn:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How do you solve a rational expression:
(7x+3)/(x^2 - 8X+15) + (3x)/(x-5) = 1/(3-x)
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(7x+3)/[(x-3)(x-5)] + (3x)/(x-5) = -1/(x-3)
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Multiply thru by (x-3)(x-5) to get:
(7x+3) + (3x)(x-3) = -(x-5)
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7x+3 + 3x^2 - 9 = -x + 5
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3x^2 + 8x -11 = 0
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(x-1)(3x+11) = 0
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x = 1 or x = -11/3
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Cheers,
Stan H.
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Answer by MathTherapy(10549) About Me  (Show Source):
You can put this solution on YOUR website!
How do you solve a rational expression:
7x+3/x2 - 8X+15 +3x/x-5= 1/3-x
Why is it so difficult for people to use PARENTHESES?

If it's %287x+%2B+3%29%2F%28x%5E2+-+8x+%2B+15%29+%2B+3x%2F%28x+-+5%29+=+1%2F%283+-+x%29, then: highlight_green%28matrix%281%2C7%2C+x%2C+%22=%22%2C+-+2%2F3%2C+or%2C+x%2C+%22=%22%2C+1%29%29

Answer by ikleyn(52748) About Me  (Show Source):
You can put this solution on YOUR website!
.
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Plot y = %287x%2B3%29%2F%28x%5E2+-+8x%2B15%29+%2B+%283x%29%2F%28x-5%29 (red) and y = 1%2F%283-x%29 (green)




Plot y = %287x%2B3%29%2F%28x%5E2+-+8x%2B15%29+%2B+%283x%29%2F%28x-5%29 (red) and y = 1%2F%283-x%29 (green)

~~~~~~~~~~~~~~~~~~~~~ 

%287x%2B3%29%2F%28%28x-3%29%28x-5%29%29 + %283x%29%2F%28x-5%29 = -1%2F%28x-3%29


Multiply thru by (x-3)(x-5) to get

(7x+3) + (3x)(x-3) = -(x-5)

7x+3 + 3x^2 - 9x = -x + 5

3x^2 - x - 2 = 0

x%5B1%2C2%5D = %281+%2B-+sqrt%281%5E2+-4%2A3%2A%28-2%29%29%29%2F6 = %281+%2B-+5%29%2F6.

x%5B1%5D = 1;   x%5B2%5D = -2%2F3.