x+1/3x-6=5x/6+1/x-2?

Question

i need help and fast i need to know how to solve this

Answer 1

Need parentheses.

I'm guessing you meant:

(x + 1) / (3x - 6) = (5x / 6) + (1 / x-2)

Factor the left:
(x + 1) / 3(x - 2)

Get a common denominator on the right:
(5x / 6) + (1 / x-2)
= [(x-2)(5x) + 6] / 6(x - 2)
= (5x^2 - 10x + 6) / 6(x - 2)

Now you have:
(x + 1) / 3(x - 2) = (5x^2 - 10x + 6) / 6(x - 2)

Multiply the left side by 2/2
2(x + 1) / 6(x - 2) = (5x^2 - 10x + 6) / 6(x - 2)

Now the denominators are the same, so just set the numerators equal

2(x + 1) = 5x^2 - 10x + 6
2x + 2 = 5x^2 - 10x + 6
0 = 5x^2 - 12x + 4
0 = (5x - 2)(x - 2)

5x - 2 = 0
x = 2/5

x - 2 = 0
x = 2

However, x = 2 needs to be eliminated, because it would give us a zero in the denominator.

So...
x = 2/5 is the answer

Answer 2

x+1/3x-6=5x/6+1/x-2

first multiply thru by x

x² + 1/3 - 6x = 5x²/6 + 1 - 2x

multiply thru by 6

6x² + 2 - 36x = 5x² + 6 - 12x

group like terms

11x² - 24x - 4 = 0

solve using quadratic formula

ax² + bx + c = 0
x = (-b ± √(b² - 4ac))/2a

x = (24 ± √(576 + 176))/22

x = (24 ± √(752))/22

x = (24 ± 4√47)/22

x = (12 ± 2√47)/11
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Answer 3

This would be much easier to answer if there were some parentheses in the equation so the groupings of numerators and denominators would be clear....