# Make e the subject of the formula

• February 5th 2011, 11:14 AM
Natasha1
Make e the subject of the formula
I need to make e the subject of the formula

T = n(1+e) / (1-e)

Forgot how to do these complicated ones (Headbang)
• February 5th 2011, 11:28 AM
earboth
Quote:

Originally Posted by Natasha1
I need to make e the subject of the formula

T = n(1+e) / (1-e)

Forgot how to do these complicated ones (Headbang)

1. Multiply both sides of the equation by (1 - e)

2. Expand the brackets on both sides.

3. Collect all terms containing e at the LHS of the equation, all others at the RHS:

$-T \cdot e - n \cdot e = n - T$

4. Factor out e at the LHS.

5. Divide both sides of the equation by -( T + n)
• February 5th 2011, 11:34 AM
Natasha1
On point 4 you get e (- n - T) = n - T don't you?
• February 5th 2011, 11:35 AM
Natasha1
Oh so e = - 1 is this correct?
• February 5th 2011, 11:39 AM
earboth
Quote:

Originally Posted by Natasha1
Oh so e = - 1 is this correct?

Unfortunately no.

$-T \cdot e - n \cdot e = n - T~\implies~e(-T-n)=n-T$

Now divide:

$e = \dfrac{n-T}{-T-n} = \dfrac{-(T-n)}{-(T+n)} = \dfrac{T-n}{T+n}$
• February 5th 2011, 11:43 AM
Natasha1
Thanks