My brain refuses to work, LCD

[elizabethj]

We are doing review from last semester in my new class and I just can not seem to remember any of the information I need to know! This is the problem that I am having uh, problems with.

5/2x-8/9=1/18-1/3x

Hopefully that is clear, I'm not sure how to make it look like my actual problem.

So my first thought is to clear the fractions but I am not sure what the LCD would be. If I used 18, or 18x I would end up with a variable/number situation and I am not sure if that reduces/how?

This is the simplest question on the review and I just can't get it, feeling a bit like crying!

 

[elizabethj]

Never mind, I figured it out.

 

[lookagain]

We are doing review from last semester in my new class and
I just can not seem to remember any of the information I need to know! T
his is the problem that I am having uh, problems with.

5/2x-8/9=1/18-1/3x

Hopefully that is clear, I'm not sure how to make it look like my actual problem.
Use grouping symbols around the denominators that are variable expressions.
Also, space out the characters for better readability. See ** below.

So my first thought is to clear the fractions but I am not sure what the LCD would be.
If I used 18, or 18x I would end up with a variable/number situation and I am not
sure if that reduces/how?

** 5/(2x) - 8/9 = 1/18 - 1/(3x)


This is equivalent to

\(\displaystyle \dfrac{5}{2x} - \dfrac{8}{9} \ = \ \dfrac{1}{18} - \dfrac{1}{3x}\)


The LCD is 18x.

 

[HallsofIvy]

Or if you meant (5/2)x +8/9= 1/18- (1/3)x (what you wrote is properly what lookagain wrote, but people are not always "proper"), then The "least common denominator" is 18, which is divisible by all of 2, 3, 9, and 18. If you multiply both sides of the equation by 18, you get 9(5)x+ 2(8)= 1- 6(x), 45x+ 16= 1- 6x.