solve (x-5/x )-1=x+3/x

Question

e.mccormick · Answer

This is all about order of operations.  You need to get x alone.  Do you know how you would go about that?

anonymous · Answer

not really

e.mccormick · Answer

OK.  If you look at it, everything on the right has an x.  But the left is mixed up.  So why not move things over.

anonymous · Answer

could you add one to both sides

e.mccormick · Answer

Yes, but that won't get all the xes together.

e.mccormick · Answer

$\left(x-\frac{5}{x} \right)-1=x+\frac{3}{x}$
$\left(x-\frac{5}{x} \right)-\left(x-\frac{5}{x} \right)-1=x+\frac{3}{x}-\left(x-\frac{5}{x} \right)$
$-1=x+\frac{3}{x}-\left(x-\frac{5}{x} \right)$

e.mccormick · Answer

See, that gets all the Xes on one side.  Now, it still needs to be simplified.

anonymous · Answer

-2/x on the right side

e.mccormick · Answer

Yes!
$-1=-\frac{2}{x}$
So, what do you think will be good to do next?

anonymous · Answer

could you multiply both sides by -2

e.mccormick · Answer

Well, that would still leave the x on the bottom of a fraction.  The goal here is to get rid of the fraction next.

anonymous · Answer

divide by-2

e.mccormick · Answer

Still leaves a fraction...  so not the best choice.  Great you are thinking about it, but there is a better choice.

anonymous · Answer

i dont know

e.mccormick · Answer

Ever heard about multiplying by the inverse to get rid of a fraction?

anonymous · Answer

oh

e.mccormick · Answer

We don't need the whole inverse this time.  Mostly we just need the x.

e.mccormick · Answer

In fact... you could finish this in one step if you multiply by a negative x.  That would take care of the - on the 1 and the x under the fraction all at the same time!  =)

anonymous · Answer

so it would be x=2

e.mccormick · Answer

Yep!
$-1\cdot (-x)=-\frac{2}{x}\cdot (-x)\implies x=2$

anonymous · Answer

thanks

anonymous · Answer

wait thats not an answer choice

e.mccormick · Answer

np.  This is all about figuring out how to get the x alone and out of any fractions.  That is all about using the order of operation rules.  If you work with those more, these should be a lot easier for you.  =)

e.mccormick · Answer

Oops!  I missed one mistake!

anonymous · Answer

8

 0

 −1

 −8

e.mccormick · Answer

Look at this again: $-1=x+\frac{3}{x}-\left(x-\frac{5}{x} \right)$

The negative distribution! $-1=x+\frac{3}{x}-x+\frac{5}{x} $

e.mccormick · Answer

$-1=\frac{8}{x}$

anonymous · Answer

isnt it x-5/x

e.mccormick · Answer

The - outdide the parentisis distributes to both.
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