Finding the Solution for x in a Fractional Equation

  • Thread starter Amaz1ng
  • Start date
In summary, the conversation is about solving the equation x/m - 1/n = 3x/mn for x. The solution involves bringing all the terms containing x on one side of the equation and factoring it out. The final answer is m/n - 3. The conversation also discusses the concept of multiplying through by a common denominator and finding the LCM.
  • #1
Amaz1ng
42
0

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.
 
Physics news on Phys.org
  • #2
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 :)
 
  • #3
[itex]\frac{x}{m}\,-\,\frac{1}{n}\,=\,\frac{3x}{mn}[/itex]

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:

[itex]xn\,-\,m\,=\,3x[/itex]

but I don't see how.
 
  • #4
Rewrite your equation as:
[tex]xn - 3x = m[/tex]
[tex]x (n-3) = m[/tex]
Do you see it now? The key idea is to bring all the 'x' terms on one side so you can factor it out.
 
  • #5
I get these parts:

[itex]
xn\,-\,m\,=\,3x
[/itex]

[tex]
x (n-3) = m
[/tex]

But how do you get it from here to here:

[itex]
\frac{x}{m}\,-\,\frac{1}{n}\,=\,\frac{3x}{mn}
[/itex]

to here:

[itex]
xn\,-\,m\,=\,3x
[/itex]
 
  • #6
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
 
  • #7
Amaz1ng said:
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.
 
  • #8
Ok I think I got it...I was thinking about it like a fraction.

Thanks alot. :D
 

1. What is the purpose of solving an equation for x?

Solving an equation for x allows us to find the value of the unknown variable, x, which satisfies the given equation. This is important in many areas of science, as it allows us to make predictions and solve problems.

2. What are the steps involved in solving an equation for x?

The first step is to collect all the terms with x on one side of the equation and all the constants on the other side. Then, we use inverse operations to isolate x. Finally, we check our solution by plugging it back into the original equation.

3. Can you solve any equation for x?

Yes, as long as the equation follows the rules of algebra, it can be solved for x. However, some equations may have complex or imaginary solutions, which may not be applicable in certain situations.

4. Are there any common mistakes to avoid when solving an equation for x?

One common mistake is forgetting to perform the same operation on both sides of the equation. This can lead to incorrect solutions. It is also important to always check your solution by plugging it back into the original equation to ensure it is valid.

5. How can solving equations for x be useful in everyday life?

Solving equations for x is useful in many practical situations, such as calculating discounts or solving for missing measurements in recipes. It also helps us understand and analyze data in fields such as economics, physics, and chemistry.

Similar threads

  • Introductory Physics Homework Help
Replies
24
Views
837
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
597
  • Introductory Physics Homework Help
Replies
19
Views
923
  • Differential Equations
2
Replies
52
Views
416
  • Introductory Physics Homework Help
Replies
2
Views
648
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
771
  • Introductory Physics Homework Help
Replies
1
Views
3K
  • Introductory Physics Homework Help
2
Replies
36
Views
608
Back
Top