subtracting fractions

[jedwa1216]

Hello,

Can you please explain to me how this works. (1)/(x(x+3) - (1)/(3x) = (-1)/(3(x+3)) This should be right but I don't know how to work it out. Thanks, Jeff.

This is a better picture of the problem. I took this from the calculus board since it is not really calculus at this point. Thanks. Sorry I don't know how to insert the image.

 

[Loren]

Hello,

Can you please explain to me how this works. (1)/(x(x+3) - (1)/(3x) = (-1)/(3(x+3)) This should be right but I don't know how to work it out. Thanks, Jeff.

This is a better picture of the problem. I took this from the calculus board since it is not really calculus at this point. Thanks. Sorry I don't know how to insert the image.

Can't make much sense out of this. It seems that you have stated a problem as...
\(\displaystyle \frac{\frac{1}{x+3}-\frac{1}{3}}{x}=\frac{1}{x(x+3)}-\frac{1}{3x}=\frac{-1}{3(x+3)}\)

You are not showing a couple of intermediate steps, but the end result is correct.

 

[jedwa1216]

Can you show me how to do it? I really need to understand how to get the answer. thanks, Jeff.

 

[Deleted member 4993]

Can you show me how to do it? I really need to understand how to get the answer. thanks, Jeff.

Do you understand the first step?

\(\displaystyle \frac{\frac{1}{x+3} - \frac{1}{3}}{x} \ = \ \frac{1}{x(x+3)} \ - \ \frac{1}{3x}\)

 

[jedwa1216]

Yes, I see how that works but I don't understand how the answer is derived from the last two fractions. Thanks.

 

[Deleted member 4993]

Yes, I see how that works but I don't understand how the answer is derived from the last two fractions. Thanks.

Now you will do equivalent operation when you subtract fractions (without calculator).

What is the LCM of the denominators [x(x+3) and 3x]?

 

[Loren]

\(\displaystyle \frac{\frac{1}{x+3}-\frac{1}{3}}{x}=\frac{1}{x(x+3)}-\frac{1}{3x}=\frac{1}{x(x+3)}\cdot\frac{3}{3}-\frac{1}{3x}\cdot\frac{(x+3)}{(x+3)}=???\)

 

[jedwa1216]

I just get a denominator of (3x(x+3)). with a numerator of -X-0. I don't see how to get a numerator of -1 and a denominator of 3x+3. Thanks for your help. Jeff.

 

[Deleted member 4993]

I just get a denominator of (3x(x+3)). with a numerator of -X-0. I don't see how to get a numerator of -1 and a denominator of 3x+3. Thanks for your help. Jeff.

Your denominator should be -

3x(x+3)

you have in the numerator

-x

If you divide numerator and the denominator by x, you are left with:

\(\displaystyle \frac{-1}{3(x+3)}\)

This is basic algebra - you need to review these thoroughly before embarking on calculus.