How do i solve this Math Problem???

My answer is
X = 1 - 4x/(6-3x)
or simplify it further: X = (6 - 7x)/(6 - 3x)
here's how I did it:
3x/2 - 2x/(X-1) = 3
get the LCD of the left side of the equation which is 2(X-1)
simplify the left side further and we get [3x(X -1) - 2x(2)]/[2(X-1)]
the equation will be [3x(X -1) - 2x(2)]/[2(X-1)] = 3
to cancel out the denomenator on the left side of the equation,
we multiply both sides of the equation by [2(X-1)]
and the result will be [3x(X -1) - 2x(2)] = 3[2(X-1)]
by simplifying further the result will be 3x(X -1) - 4x = 6(X-1)
let's transfer the 3x(X -1) to the right side of the equation
by subtracting both sides with 3x(X -1)
the result will be -4x = 6(X-1) - 3x(X -1)
on the right side of the equation we can factor out (X -1)
the result will be -4x = (6 - 3x)(X -1)
divide both sides of the equation by (6 - 3x) to even further isolate
the X... ^_^ the result will be -4x/(6 - 3x) = X - 1
add 1 to both sides of the equation to cancel out the minus 1
on the right side *********(^_^)****************
the answer will be -4x/(6 - 3x) + 1 = X
or simply X = 1 - 4x/(6 - 3x)

try it yourself!

3x/2 - 2x/(x - 1) = 3
2[x - 1][3x/2 - 2x/(x - 1)] = 2[x - 1][3]
3x[x - 1] - 2[2x] = 6[x - 1]
3x^2 - 3x - 4x = 6x - 6
3x^2 - 7x - 6x + 6 = 0
3x^2 - 13x + 6 = 0
x = [-b ±√(b^2 - 4ac)]/2a

a = 3
b = -13
c = 6

x = [13 ±√(169 - 72)]/6
x = [13 ±√97]/6
x = [13 ±9.84]/6 (approx.)

x = [13 + 9.84]/6
x = 22.84/6
x = 3.807

x = [13 - 9.84]/6
x = 3.16/6
x = 0.527

∴ x ≈ 0.527 , 3.807

if x and X are different,then you can't get any value for X,but u can get a relation in x and X.i.e.
3xX-6X-7x+6=0
If x and X are same, u will get a quadratic in x i.e.
3x^2-13x+6=0
it will give x=[13+(157)^1/2]/6
and x=[13-(157)^1/2]/6

X-1 appears in denominator. Therefore, X=1 is not valid.
(3x/2) - 2x/(x-1) = 3
Or,
{3x(x-1) - 2*2x}/{2*(x-1)} = 3
Or, 3x(x-1) - 2*2x = 3*2*(x-1)
Or, 3x^2 - 3x - 4x = 6x - 6
Or, 3x^2 - 7x = 6x - 6
Or, 3x^2 -7x -6x + 6 = 0
Or, 3x^2 - 13x + 6 = 0
This is a quadratic equation of form ax^2+bx+c = 0
where a=3, b=-13,c=6
Discriminant D=b^2-4ac = (-13)^2 - 4*3*6 = 169 - 72 = 97
x = {-b ±√D}/(2a)
x = {13 ±√97}/(2*3) = (13 ± 9.85)/6
= 22.85/6, 3.15/6
= 3.81, 0.525

Ans: 3.81, 0.525

3x^2 - 7x - 6(x - 1) = 0 on taking L.C.M and crossmultiplying

3x^2 - 13x + 6 = 0

x = [13 ±√(169 - 72)]/6

x = [13 ±√97]/6