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How does X in this equasion equals to 2 if 2-2=0 and you can't devide by zero? (x-1)/(x-2)-2/x=1/(x-2)

Guest Oct 8, 2017

#1**+2 **

\(\frac{x-1}{x-2}-\frac{2}{x}\,=\,\frac{1}{x-2}\)

First let's get a common denominator.

\(\frac{(x)(x-1)}{(x)(x-2)}-\frac{2(x-2)}{(x)(x-2)}\,=\,\frac{1x}{(x)(x-2)}\)

We can multiply through by the denominator....however....you are right that x can't be 2 !

Also x can't be 0 . If we plug in 0 or 2 for x into the original equation, we will get an undefined result. Before we multiply through by the denominator, we must say that **x ≠ 0 and x ≠ 2 **.

\((x)(x-1)-2(x-2) \,=\,1x\) Distribute the x and the -2 .

\(x^2-x-2x+4 \,=\,x\) Subtract x from both sides and combine like terms.

\( x^2-4x+4 \,=\,0\) Factor the left side and solve for x .

\((x-2)^2=0 \\~\\ x-2=0 \\~\\ x=2\)

But, x cannot be 2 because it causes a zero in the denominator of the original problem.

So there is **no solution**.

hectictar Oct 8, 2017