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