+0

# How does this work?

+1
146
1

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
Sort:

#1
+6943
+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
edited by hectictar  Oct 8, 2017

### 7 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details