How do you solve rational equations $2/x-2 = x/(x-1) - 2$ ?

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Answer 1 · 2018-04-30T21:19:17

No solutions

Add 2 to both sides

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

$2(x-1)=x^2$

$2x-2=x^2$

$x^2-2x+2=0$

Use the formula

$x=[-(-2)\pmsqrt((-2)^2-4xx1xx2)]/2$

$x=[2\pmsqrt(-4)]/2$

Cannot find the square root of a negative number so there are no solutions.

How do you solve rational equations 2/x-2 = x/(x-1) - 22/x-2 = x/(x-1) - 2?