SOLUTION: This is a problem I need help with.[(1/9)+(1/3x)] / [(x/9)-(1/x)]

Question 186669: This is a problem I need help with.[(1/9)+(1/3x)] / [(x/9)-(1/x)]
Found 2 solutions by vleith, jim_thompson5910:
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
In order to simplify let's simplify the numerator and denominator separately first

Simplifying the numerator :

Start with the numerator. Take note that the LCD

Multiply the first fraction by

Multiply the second fraction by

Add the fractions.

So where

----------------------------------------------------------

Simplifying the denominator :

Start with the denominator. Take note that the LCD

Multiply the first fraction by

Multiply the second fraction by

Subtract the fractions.

So where

---------------------------------------------------------------

Now that we've simplified the numerator of , we then get:

Start with the simplified expression.

Multiply the first fraction by the reciprocal of the second fraction.

Factor to get

Combine the fractions.

Highlight the common terms.

Cancel out the common terms.

Simplify

==================================================================

Answer:

So simplified to which in turn simplified to

So in short, simplifies to

In other words, where , , or
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