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)   (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)
--------
(7x+3)/[(x-3)(x-5)] + (3x)/(x-5) = -1/(x-3)
-------
Multiply thru by (x-3)(x-5) to get:
(7x+3) + (3x)(x-3) = -(x-5)
-------------------------------
7x+3 + 3x^2 - 9 = -x + 5
----------------------------------
3x^2 + 8x -11 = 0
----
(x-1)(3x+11) = 0
-----
x = 1 or x = -11/3
--------------------------
Cheers,
Stan H.
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Answer by MathTherapy(10549)   (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 , then:  

Answer by ikleyn(52750)   (Show Source): You can put this solution on YOUR website!
 .

.







Plot y =  (red) and y =  (green)













Plot y =  (red) and y =  (green)





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 +  = 


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

 =  = .

 = 1;    = .





 

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