Finding the Solution for x in a Fractional Equation

[Amaz1ng]

Homework Statement

Hello I have this problem here:x/m - 1/n = 3x/mn. Solve for x.

Homework Equations

The Attempt at a Solution

I got it to this level:

xn = 3x + m

and the final answer is m / n - 3.

How do I go about getting the final answer? I just want to know what I'm missing because I don't see how to reduce it to the final answer. I always have these problems with fractions and division.

 

[Fightfish]

What you want to do is to be able to factor out x. In such questions, we usually seek to reduce the equation to a form ax = b, where a and b are independent of x.
To do that, we clearly need all the terms containing x on one side to be able to factor it out. Please carry on :)

 

[Amaz1ng]

$\frac{x}{m}\,-\,\frac{1}{n}\,=\,\frac{3x}{mn}$

When someone says to multiply through by mn, what mathematics rule is that and how do you go about doing it?

Supposedly, multiplying through my mn gives:

$xn\,-\,m\,=\,3x$

but I don't see how.

 

[Fightfish]

Rewrite your equation as:
$$xn - 3x = m$$
$$x (n-3) = m$$
Do you see it now? The key idea is to bring all the 'x' terms on one side so you can factor it out.

 

[Amaz1ng]

I get these parts:

$xn\,-\,m\,=\,3x$

$$x (n-3) = m$$

But how do you get it from here to here:

$\frac{x}{m}\,-\,\frac{1}{n}\,=\,\frac{3x}{mn}$

to here:

$xn\,-\,m\,=\,3x$

 

[Amaz1ng]

Ok the issue is that I'm thinking about it like this:

if you subtract two fractions then you have to find the LCM or some common denominator. How do you do that with this or am I thinking about it wrong?

mn * x/m - mn * 1/n

What do you do with this? ;o

 

[ideasrule]

Ok the issue is that I'm thinking about it like this:

if you subtract two fractions then you have to find the LCM or some common denominator. How do you do that with this or am I thinking about it wrong?

mn * x/m - mn * 1/n

What do you do with this? ;o

The first term is m times n, times x, divided by m. m divided by m is 1, so it reduces to nx for the same reason that 2*3/2 = 3.

 

[Amaz1ng]

Ok I think I got it...I was thinking about it like a fraction.

Thanks a lot. :D