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Why is the following not possible?

$$\frac{2x-1}{2x}\neq4x-2$$

And the following method not correct?

$$\bigg(\frac{2x-1}{2x} + \frac{1}{1}\bigg)-1\equiv\frac{2x-1}{2x}$$

Cross multiplying:

$$\big(1[2x-1]+1[2x]\big)-1$$

With the result:

$$2x-1+2x-1=4x-2$$

My question, essentially is, is the following possible:

$$\frac{a}{b}+\frac{c}{d}\equiv ad+bc?$$

I know it is true for the following:

$$\frac{a}{b}=\frac{c}{d}\equiv ad=bc$$

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    What? Of course $\frac{2x-1}{2x}\neq 4x-2$ in general, just consider $x=1$. I'm confused why you say it is "not possible".2012-09-19
  • 0
    Perhaps my phraseology is a little misleading. I am attempt to question the method by which I got to the result.2012-09-19

3 Answers 3