Question 30346: x+3/5= x+1/x-3 This ia a rational fraction and i cant seem to find the right answer is there anyway you could help me.! Please and thank you
Answer by Fermat(136)   (Show Source):
You can put this solution on YOUR website! x+3/5= x+1/x-3
There ae two ways to interpret the above eqn
1) x+(3/5)= x+(1/x)-3
2) (x+3)/5= (x+1)/(x-3)
You should use bracketed terms to avoid ambiguity, thanks.
Solution for case 1)
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x+(3/5)= x+(1/x)-3
The denominators in your fractions are x and 5, so multiply all the terms by 5x (the product of the denominators). This gives,
5x² + 3x = 5x² + 5 - 15x
18x = 5
x = 5/18
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Solution for case 2)
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(x+3)/5= (x+1)/(x-3)
cross-multiply
(x+3)(x-3) = 5(x+1)
x² - 9 = 5x + 5
x² - 5x - 14 = 0
(x+2)(x-7) = 0
x = -2, x = 7
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