4/x-5/3=x/6?

Question

find all solutions

Answer 1

4/x - 5/3 = x/6 simplify by multiplying both sides by x
4- 5x/3 = xsquared/6 then simplify by multiplying both sides by 6
24 -10x = xsquared, which equal to
0 = xsquared +10x -24, which is
0 = (x+12)(x-2)
answer = -12,+2

Answer 2

first you have top get rid of the fractions, so multiply through by the common denominator, which is 6x

and you get

24 -10x = x^2

its a quadratic, so rearrange it and factor

0 = x^2 + 10x - 24

0 = ( x - 2)(x + 12)

so x = 2 or x = -12

and check to see if they work:

4/2 - 5/3 = 2/6
2=2/6 + 10/6
2=12/6
2=2

and

4/-12 - 5/3 = -12/6
-1/3 - 5/3 = -2
-6/3 = -2
-2 = -2

so sure enough they both work

Answer 3

(4 / x) - (5 / 3) = (x / 6)
Multiply everything by 6
(24 / x) - (30 / 3) = x
(24 / x) - 10 = x
Multiply everything by x
24 - 10x = x^2
Rearrange...
x^2 + 10x - 24 = 0
Factor that out....
(x + 12) (x - 2) = 0

The solutions are (x = -12) and (x = 2).

Answer 4

lcd is 6x

24-5(2x)=x^2
24-24-10x+10x=x^2+10x-24

x^2+10x-24=0
(x+12)(x-2)=0
x=-12 or 2