Simple rearranging of an equation

[smulc]

I need to rearrange an equation to end up with something else. It's supposed to be an easy question but I can't see what I'm doing wrong. Posting the actual text here would mess up the formatting so I posted a screenshot to keep it neat, I hope that's okay. Have I done the entire thing wrong or am I missing something simple?

 

[crotical]

You can definitely divide by b

 

[smulc]

That's good to know, that's what I was going to do but for some reason I got into my head that I couldn't. Thanks!

 

[crotical]

You need to only worry when b=0 , as division by 0 is not defined.

 

[e^(i Pi)+1=0]

You can rearrange this equation in only two steps. Although the second step isn't nearly as obvious. Remember, you're not limited to only shunting around the symbols that you start with, you can do anything to the equation, as long as you do it to both sides...

 

[smulc]

Could you give me a hint on the quicker way to do it please? I can't see it. The question doesn't require a minimal number of steps so I've already answered it the longer way, I'm just curious what I'm missing though.

 

[Deneb Cyg]

It's a bit faster if you keep in mind that \frac{am^2T^4}{bd^2} can be split into \frac{a}{b}x\frac{m^2T^4}{d^2}

Then you just have to divide C by \frac{m^2T^4}{d^2} to get the answer.

Since you are solving for a fraction and not a single variable you never need to isolate a or b on one side of the equation.

 

[smulc]

That makes sense now, think I need a bit more practice to make sure I pick things like that up. Thanks for explaining.

 

[e^(i Pi)+1=0]

Here's how I did it...it's 3 steps if you count simplifying

1. multiplied both sides by d²

2.divide both sides by m²T⁴

3. simplify the weird looking side and see what you end up with...