# Question regarding frations with variables?

#### 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!!

#### Pim

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

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#### fetuslasvegas

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

#### allsmiles

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??

#### Pim

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

#### e^(i*pi)

MHF Hall of Honor
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 $$\displaystyle \frac{5}{6x} + \frac{1}{2} = \frac{5}{3x}$$

Multiply through by $$\displaystyle 6x$$

$$\displaystyle 5 + 3x = 10$$

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

#### fetuslasvegas

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

#### harish21

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

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

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

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

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

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

cross multiplication gives:

$$\displaystyle 6x = 10$$

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

Clear??

#### fetuslasvegas

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

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

Multiply through by $$\displaystyle 6x$$

$$\displaystyle 5 + 3x = 10$$

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

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.

#### e^(i*pi)

MHF Hall of Honor
I'm still really confused, would you mind putting in words because I'm not understanding what's going on with just numbers (Worried)
You are given: $$\displaystyle \frac{5}{6x} + \frac{1}{2} = \frac{5}{3x}$$

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

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

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

fetuslasvegas