how do you solve 1/4= 3- 2x-1/x+2 algebraically ?

1/4 = 3 - 2x - 1 / (x + 2)

1/4 * (x+ 2) = 3 -2x -1


x + 2 = 4 * ( 3 -2x - 1)

x + 2 = 12 - 8x - 4

x + 8x = 8 - 2

9x = 6

x = 6/ 9 = 2/3

As you have given it , question MUST be read as :-

1/4 = 3 - 2x - (1/x) + 2

If I was a betting person I would lay odds that this is NOT what you mean ?

1/4 = 3 - (2x - 1)/(x + 2)
3 - 1/4 = (2x - 1)/(x + 2)
(x + 2)(12/4 - 1/4) = 2x - 1
(x + 2)(11/4) = 2x - 1
11(x + 2)/4 = 2x - 1
11(x + 2) = 4(2x - 1)
11*x + 11*2 = 4*2x - 4*1
11x + 22 = 8x - 4
11x - 8x = -22 - 4
3x = -26
x = -26/3

Hi!

1/4= 3- 2x-1/x+2

multiply 4 yields

1 = 12 - 8x - 4/x + 8

now group them on one side

-8x - 4/x +19 = 0

now, multiply x yields

-8x^2 + 19x -4 = 0

using x = (-b + sqrt(b^2 - 4ac))/ 2a and (-b - sqrt(b^2 - 4ac))/ 2a

and subsituting a=-8, b=19 and c=-4,

you should get the answer. try it!

0.25 = 3 - 2x - 1/(x+2)

lets multiply the whole thing by x+2
0.25x + 0.5 = 3x + 6 - 2x^2 - 4x - 1
2x^2 + 1.25x - 4.5 = 0
x=1.219
x=-1.844

2x + 1/x = 5 - 1/4 = 4 3/4 = 19/4

mult by 4x:

8x^2 + 4 = 19x

8x^2 - 19x + 4 = 0