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)
First let's get a common denominator.
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.