[MOVED] why is 1/x + 1/x^2 = x^2/(1 - x)

[unregistered]

I know that there are some steadfast rules that I forgot about for why:

I totally forgot this,

Thanks.

 

[stapel]

On what basis do you believe that \(\displaystyle \L \frac{1}{x}\,+\,\frac{1}{x^2}\), which simplifies as \(\displaystyle \L \frac{x\,+\,1}{x^2}\), is equal to \(\displaystyle \L \frac{x^2}{1\,-\,x}\)? They don't even have the same domains.

Please reply with clarification. Thank you.

Eliz.

 

[unregistered]

Oh no, I need to go back a step or 2 or 18, why does it simplify to

That is why I posted this in arithmetic b/c I forgot the simple stuff.

 

[skeeter]

Oh no, I need to go back a step or 2 or 18, why does it simplify to

That is why I posted this in arithmetic b/c I forgot the simple stuff.

\(\displaystyle \L \frac{1}{x} + \frac{1}{x^2} =\)

common denominator is \(\displaystyle \L x^2\) ...

\(\displaystyle \L \frac{x}{x^2} + \frac{1}{x^2} = \frac{x+1}{x^2}\)

 

[unregistered]

why does x become the numerator in the first fraction? Sorry for the dumb question.

 

[skeeter]

\(\displaystyle \L \frac{1}{x} \cdot \frac{x}{x} = \frac{1 \cdot x}{x \cdot x} = \frac{x}{x^2}\)

 

[unregistered]

nice, thx.

 

[Denis]

When in doubt, Reg, try a "simple":
1/2 + 1/4 = 2/4 + 1/4
similarly:
1/x + 1/x^2 = x/x^2 + 1/x^2