Rational equation?

Question

I can't seem to work this one out

2/x-2 = x/(x-1) - 2

I wrote that wrong

(2/x-2) = (x/x-1) - 2

Answer 1

Is it 2/(x-2) or 2/x - 2 ?

If its 2/(x-2) = x(x-1) - 2, then
2 = (x-2) x (x-1) - 2
2 = x^3 - 3x^2 + 2x - 2
x^3 - 3x^2 + 2x = 0

Answer 2

Solving for x:

2/x-2 = x/(x-1) - 2

2/x = x/(x-1) (add 2 to both sides)

2(x-1)/x = x (multiply both sides by (x-1))

2(x-1) = x² (multiply both sides by x)

2x-2 = x² (expand brackets)

x² - 2x + 2 = 0 (transfer all values to one side of equation)

(x-1)(x-1) = 0 (factorising - always check by expanding)

x=1 (if x = 1 then the above equation will be satisfied)

Answer 3

if this was your equation:

2 over
x

minus 2

=

x over
(x-1)

minus 2



This is what I got:

2x-2= x squared (little 2 goes to the upper right of the x)


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Answer 4

2/(x-2)=[x-2(x-1)]/(x-1)
2/(x-2)=[x-2x+2]/(x-1)
2/(x-2)=(-x+2)/(x-1)
2(x-1)=(x-2)((-x+2)
2x-2=-(x-2)^2
2x-2=-(x^2-4x+4)
2x-2=-x^2+4x-4
x^2-2x+2=0
x=[2+/-(4-8)]/2
=1+/-i