please help me solve this problem!?

Question

((4x)/(x-2)) = x + ((8)/(x-2))

please work it out!!

2 is wrong!!

Answer 1

4x/ (x-2) = x + (8/(x-2))
4x/ (x-2) = (x2-2x)/(x-2) + (8/(x-2)
4x/ (x-2) = (x2-2x+8) / (x-2)
4x = x2-2x+8
x2-6x+8 = 0
(x-4) (x-2) = 0
x = 4 or x = 2

Answer 2

4x / (x - 2) = x + 8 / (x - 2)
4x = x (x - 2) + 8
4x = x² - 2x + 8
x² - 6x + 8 = 0
(x - 4) (x - 2) = 0
x = 4 is the acceptable answer. (x ≠ 2)

Answer 3

minus 8/(x-2) from both sides therefore:

(4x-8)/(x-2)=x

or

(4x-8)/(x-2) - x(x-2)/(x-2)=0

therefore simplifying:

(4x-8-x(x-2))/(x-2)=0

therefore 4x-8-x(x-2)=0

4x-8-x^2+2x=0 or x^2-6x+8 = 0; which is the same as (x-2)(x-4) = 0

therefore x = 2 OR 4; but x cannot equal 2 since there is (x-2) as the denominator; hence

x = 4

Answer 4

((4x)/(x-2)) = x + ((8)/(x-2))

multiply both sides by (x-2), then cancels out
the numerator and denominator with (x-2).

4x = (x-2)x + 8

4x = x²-2x + 8

x²-6x + 8 = 0

By Quadratic Equation:

x = [-b±√(b²-4ac)]/2a

x = 4

To chech this out:

((4x)/(x-2)) = x + ((8)/(x-2))

Substituting the value of x, we have:

(4(4)/(4-2)) = 4 + (8/(4-2)

16/2 = 4 + 8/2

8 = 4 + 4

8 = 8

LHS = RHS

Answer 5

4x/x-2=x + 8/x-2
= 4x/x-2=x square -2x +8 /x-2
= 4x= x square -2x +8
= 2x = x square + 8
=x=x square + 8 /2

Answer 6

4x/(x-2) = x+(8/(x-2)) *(x-2)
4x=x(x-2)+8
x^2 - 6x + 8 = 0
x1=2 and x2=4
Your answer is X = 4

Answer 7

4x / (x - 2 ) = 8 / (x - 2 )
4 x = 8
x = 2

Answer 8

((4x)/(x-2)) = x + ((8)/(x-2))
((4x)/(x-2)) - ((8)/(x-2)) = x
(4x-8)/(x-2) = x
4x-8 = x(x-2)
4x-8 = (x^2)-2x
(x^2)-6x+8 = 0
(x-2)(x-4) = 0
x = 2 , x = 4

Answer 9

((4x)/(x-2)) = x + ((8)/(x-2))

4x/(x-2) = [x(x-2)+8]/(x-2)

[x^2-2x+8]/(x-2) - 4x/(x-2) = 0

[x^2-6x+8]/(x-2) = 0

[(x-4)(x-2)]/(x-2) = 0

x-4 = 0

x=4

Answer 10

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