Rearrange Equations: Making J the Subject - Need Help

[peter_pan]

SO here is the problem

I am wondering how to make J the subject ?

I have tried making J/2 and 4a/3 into a single fraction but so far nothing.I am doing something wrong somewhere.


Any suggestions ?

 

[Mark44]

Here it is so I can see it better:
$$V = \frac{\frac{J}{2} + \frac{4a}{3}}{L}$$

Multiply both sides by L.
Subtract 4a/3 from both sides.
Multiply both sides by 2.

 

[Architeuthis Dux]

Sure, I can help with rearranging equations to make J the subject. First, let's clarify what we mean by "making J the subject." This simply means isolating J on one side of the equation, with all other variables and numbers on the other side. To do this, we can use algebraic operations such as addition, subtraction, multiplication, and division.

Let's take a look at the equations you provided. You mentioned trying to make J/2 and 4a/3 into a single fraction, but you were unsuccessful. It's important to remember that when combining fractions, we need to have a common denominator. So, for J/2 and 4a/3, we can rewrite them as (3J/6) and (8a/6), which have a common denominator of 6. Now, we can combine them into a single fraction: (3J+8a)/6.

Next, we need to isolate J on one side of the equation. We can do this by subtracting 8a from both sides, giving us (3J+8a)/6 - 8a = 0. Simplifying this, we get (3J - 40a)/6 = 0. Now, we can multiply both sides by 6 to get rid of the fraction, giving us 3J - 40a = 0. Finally, we can add 40a to both sides to isolate J, giving us the final equation: J = 40a/3.

So, in summary, to make J the subject, we combined the fractions, isolated J on one side of the equation, and solved for J. I hope this helps! Let me know if you have any other questions or if you need further clarification.