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How do you do x+1/3 = 4/x-3?

Author :

Submitted : 2018-06-14 07:40:43    Popularity:     

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transfer all the x's to one side of the equation, and all the number values to the other. Then solve for X. x + 1/3 = 4/(x - 3) 3x(x - 3) + (x - 3) =

Answers:

transfer all the x's to one side of the equation, and all the number values to the other. Then solve for X.

x + 1/3 = 4/(x - 3)
3x(x - 3) + (x - 3) = 12
3x^2 - 8x - 15 = 0
Solutions:
x = 4/3 - sqrt(61)/3
x = 4/3 + sqrt(61)/3

You really need to use parentheses to group things. Because division takes precedence, your equation would be interpreted as:
x + (1/3) = (4/x) - 3

However, I think you meant to group the terms as:
(x + 1)/3 = 4/(x - 3)

Cross multiply to get rid of the denominators:
(x + 1)(x - 3) = 3*4
x² - 3x + x - 3 = 12
x² - 2x - 15 = 0

Factor that:
(x - 5)(x + 3) = 0

That leads to two solutions:
x - 5 = 0
x = 5
or
x + 3 = 0
x = -3

Answer:
x = 5 or x = -3

10/3 = 4/x - x
10x = 12 - 3x^2
3x^2+10x-12 = 0
x = [-10±√244]/6
x = (-5 ± √61)/3

You have to isolate x on one side of the equals sign. Consider this:

X + 2 = 10

By subtracting 2 from both sides of the equation, you isolate X.

X + 2 = 10
X + 2 (- 2) = 10 (- 2)
X = 8

So you have to get x's on one side and non-x's on the other. You could start by subtracting 1/3 from both sides:
x + 1/3 = 4/x - 3
x + 1/3 (- 1/3) = 4/x - 3 (- 1/3)

Combine like terms
x + (1/3 - 1/3) = 4/x + (-3 -1/3)
x = 4/x - 2 2/3

Now the left side of the equation has no non-x values, however the right side still contains both x values and non-x values, so you must do the same thing you just did, but with the "4/x" on the right side.

I'll leave off here and let you solve the rest of the way.

x+1/3 = 4/x-3
ambiguous. best guess
x + (1/3) = (4/x) - 3
x – (4/x) = –3 – (1/3) = –10/3
x² + (10/3)x – 4 = 0
x = 0.937, −4.27

another guess
(x+1) / 3 = 4 / (x-3)
12 = (x+1)(x–3)
x² – 2x –3 = 12
x² – 2x – 15 = 0
(x – 5)(x + 3) = 0
x = 5, –3



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