I think this is simple but I just cant work out how

[oliver.smith8]

how does \frac{1/a -1/b}{1/a+1/b}= \frac{b-a}{b+a}

Ive been trying to work this out for ages

thanks

 

[Tac-Tics]

It's simple algebra. Here's a few hints.

The right hand side, as given, is this:

\frac{\frac{1}{a} - \frac{1}{b}}{\frac{1}{a} + \frac{1}{b}}

But this can be written more clearly as:

(\frac{1}{a} - \frac{1}{b})(\frac{1}{a} + \frac{1}{b})^{-1}

From there, apply algebraic operations to this expression until it equals the right hand side.

 

[Gigasoft]

Think about what value you need to multiply the left hand side with to make it equal the right hand side.

 

[elect_eng]

Multiply by ab in both the numerator and the denominator. This is multiplying by one.