Need help on solving algabraic fractions

Hi there, I need with this algabraic maths question, i know the answer, but i cant understand how to get it... here it is, thanks in advance,

(x/2+x) / ( 2 + ( x / 2+x))

The answer is x / 4 + 3x

Im totally lost, i would appreciate any help you guys could offer, thanks again!

You have posted:

. . . . .\(\displaystyle \Large{\frac{\frac{x}{2}\mbox{ }+\mbox{ }x}{2\mbox{ }+\mbox{ }(\frac{x}{2}\mbox{ }+\mbox{ }x)}}\)

Is this what you meant?

Thank you.

Eliz.

sorry, this is what it should read as...

Sorry about that, it should read thus...

( x / (2+x) ) / (2 + (x / (2+x) ) )

There are at least a couple of different methods for working this sort of exercise, but the one my students usually prefer is to multiply through, top and bottom, by the overall common denominator. In this case, that would be "2 + x".

So multiply through by 2 + x:

. . . . .\(\displaystyle \Large{\left(\frac{\frac{x}{2\mbox{ }+\mbox{ }x}}{2\mbox{ }+\mbox{ }\frac{x}{2\mbox{ }+\mbox{ }x}}\right)\mbox{ }\left(\frac{\frac{2\mbox{ }+\mbox{ }x}{1}}{\frac{2\mbox{ }+\mbox{ }x}{1}}\right)}\)


. . . . .\(\displaystyle \Large{=\mbox{ }\frac{x}{2(2\mbox{ }+\mbox{ }x)\mbox{ }+\mbox{ }x}\)

Then go from there.

Eliz.

I appreciate that, but i still cant quite understand it.

to cross multiply that algabraic fraction, for the numerator, would you proceed with (x / (2+x)) * ( (2+x) / 1) ) i dont understand how that gives x.

Could you walk me through it all?

Ohh i see it now, sorry, it's just clicked!

Can i ask one question though, by multiplying ( x / (2+x) ) * ( (2+x) / 1) ) I seem to get x / (4 + 4x + x2).

You're multiplying, simplifying, factoring, and then cancelling. (Well, you still need to do that last two steps.)

Instead, cancel first; then multiply.

This is the point of multiplying through, top and bottom, by the overall common denominator: through cancellation, you will thus have simplified things considerably.

Eliz.