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sorry about the lack of a graph shown

fig 10. shows a sketch of the graph $\displaystyle y=\frac{1}{x}$

i) sketch the graph $\displaystyle y=\frac{1}{x-2}$

ii) find the x-coordinates of the points of intersection of the graphs of $\displaystyle y=x$ and $\displaystyle y=\frac{1}{x-2}$

im not sure about the translation of this graph for question i.

question ii. i got as far as $\displaystyle (x-1)^2-1=1$

but then got $\displaystyle (x-1)^2=0$

which is wrong, can someone explain why $\displaystyle (x-1)^2=2$ is right?

also how would i position these points on sketch drawn in i. ?

thanks alot if you can help as this is the last bit of revision im doing for tomorrow!