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## Homework Statement

Is there a way to show that the function [itex]\frac{2x^{2}}{x-2}[/itex] is/is'nt one to one, non graphicaly (without drawing the graph)?

## The Attempt at a Solution

I tried to following: To determine whether this function is one to one, look at what happens if two values of x give the same y: suppose [itex]2a^{2}/(a-2)= 2b^{2}/(b-2)[/itex]. Multιply both sides by [itex](a-2)(b-2)[/itex] to get [itex]2a^{2}(b-2)= 2b^{2}(a-2)[/itex]. That is the same as [itex]2a^{2}b-2a= 2b^{2}a-2b[/itex]. Trying to show, that that two different values of x cannot give the same y (this is an adaptation sugested by HallsofIvy on a similar problem). But got stuck.

Help much needed here :)

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