# Thread: Question regarding frations with variables?

1. ## Question regarding frations with variables?

Hello, I feel ridiculous asking this question but I just cannot remember.

This is my problem:

5/6x+1/2=5/3x

I know I am supposed to get the common denominator, but how do I do that when the X variable is on one denominator and not the other?

Thank you!!

2. I feel that, rather than getting the common denominatior and cross-multiplying, this question is better solved by moving the x's to the RHS

5/6x + 1/2 = 5/3x
1/2 = 5/3x-5/6x
1/2 = 10/6x-5/6x
1/2 = 5/6x
x = 6/10 = 3/5

3. My teacher gave us the answer of x=5/3, is that wrong?

4. ok, i think i have this, but not 100% sure.

step one: because it is a fraction, you owuld mult. both sides by 6x = 1.
then you would be left of with 5/1 + 1/2. which i hope you can do.

the other side is where i get confuesd. you have to cross mult, and if you did this, you would end up witha fraction again. is that what you are supost to get??

5. Originally Posted by fetuslasvegas
my teacher gave us the answer of x=5/3, is that wrong?
5/6*5/3 + 1/2 = 1 8/9
5/3*5/3 = 25/9 = 2 7/9

6. Originally Posted by fetuslasvegas
Hello, I feel ridiculous asking this question but I just cannot remember.

This is my problem:

5/6x+1/2=5/3x

I know I am supposed to get the common denominator, but how do I do that when the X variable is on one denominator and not the other?

Thank you!!
It could be due to the ambiguity. Do you mean 5/6x or 5x/6 for example?

I am assuming you mean $\frac{5}{6x} + \frac{1}{2} = \frac{5}{3x}$

Multiply through by $6x$

$5 + 3x = 10$

Solve for $x = \frac{5}{3}$

7. I'm still really confused, would you mind putting in words because I'm not understanding what's going on with just numbers

8. Originally Posted by fetuslasvegas
I'm still really confused, would you mind putting in words because I'm not understanding what's going on with just numbers

$\frac{5}{6x} + \frac{1}{2} = \frac{5}{3x}$

$\frac{5}{6x} - \frac{5}{3x} = - \frac{1}{2}$

$\frac{5}{6x} - \frac{10}{6x} = \frac{-1}{2}$

$\frac{5-10}{6x} = \frac{-1}{2}$

$\frac{-5}{6x} = \frac{-1}{2}$

cross multiplication gives:

$6x = 10$

$x = \frac{5}{3}$

Clear??

9. Originally Posted by e^(i*pi)
It could be due to the ambiguity. Do you mean 5/6x or 5x/6 for example?

I am assuming you mean $\frac{5}{6x} + \frac{1}{2} = \frac{5}{3x}$

Multiply through by $6x$

$5 + 3x = 10$

Solve for $x = \frac{5}{3}$

Yes that is what I meant, sorry I wasn't sure how to actually make fractions on here.

Ok I'm understanding a little better, the only thing I'm confused about it the 5+3x=10?? How do you get 10?

Sorry I'm terrible at fractions and math in general.

10. Originally Posted by fetuslasvegas
I'm still really confused, would you mind putting in words because I'm not understanding what's going on with just numbers
You are given: $\frac{5}{6x} + \frac{1}{2} = \frac{5}{3x}$

Multiply each term by $6x$ as this is the lowest common denominator of $2, 3 \text{ and } 6x$ (Just like 24 is the lowest common denominator of 3,4 and 6)

Multiplying by the LCD will remove the fraction to give a simple linear equation

$\frac{5}{6x} \cdot 6x + \frac{1}{2} \cdot 6x = \frac{5}{3x} \cdot 6x$

When you do some cancelling you get $5+3x=10$. Can you find x from this last equation?

11. Originally Posted by e^(i*pi)
You are given: $\frac{5}{6x} + \frac{1}{2} = \frac{5}{3x}$

Multiply each term by $6x$ as this is the lowest common denominator of $2, 3 \text{ and } 6x$ (Just like 24 is the lowest common denominator of 3,4 and 6)

Multiplying by the LCD will remove the fraction to give a simple linear equation

$\frac{5}{6x} \cdot 6x + \frac{1}{2} \cdot 6x = \frac{5}{3x} \cdot 6x$

When you do some cancelling you get $5+3x=10$. Can you find x from this last equation?

OHHH OHHH I get it!! Thank you!!!