Algebra help isolating a variable

[bonodut]

This is such a basic question that I'm embarrassed to even ask it but I don't really know where else to turn. I was reading through a derivation and one of the steps goes from $$\frac{\sqrt{a}}{n} = \frac{\sqrt{A}}{n+m}$$

to

$$n = \frac{\sqrt{a}*m}{\sqrt{A}-\sqrt{a}}$$

I'm getting really discouraged that I can't see how this follows since I know it's just simple algebraic manipulation. Anyway, if anyone could help me out with this I'd really appreciate it.

 

[aikismos]

Well, I can't give you the answer (the moderators strongly discourage working backwards), so let me suggest some steps:

1) You can use the means-extremes product theorem (sometimes referred to as cross-multiplication) to get rid of the fractions. A hint that this might be a good idea is that you're moving from an equation that has two 'n's in it to one in which you've isolated 'n'. That means at some point you are going to have use the distributive property (backwards) to factor out 'n' from a binomial.
.$$\frac{a}{b} = \frac{c}{d}$$ if and only if $$ad = bc$$
2) If you can get 'n' into a sum on one side of the equation, then you merely have to use an operation like multiplication or division to isolate it.

$$ab + ac = d \rightarrow a(b+c) = d \rightarrow a = \frac{d}{b+c}$$

 

[bonodut]

Well, I can't give you the answer (the moderators strongly discourage working backwards), so let me suggest some steps:

1) You can use the means-extremes product theorem (sometimes referred to as cross-multiplication) to get rid of the fractions. A hint that this might be a good idea is that you're moving from an equation that has two 'n's in it to one in which you've isolated 'n'. That means at some point you are going to have use the distributive property (backwards) to factor out 'n' from a binomial.
.$$\frac{a}{b} = \frac{c}{d}$$ if and only if $$ad = bc$$
2) If you can get 'n' into a sum on one side of the equation, then you merely have to use an operation like multiplication or division to isolate it.

$$ab + ac = d \rightarrow a(b+c) = d \rightarrow a = \frac{d}{b+c}$$

Thanks!