# rational equations

• Aug 11th 2009, 11:02 AM
rational equations
$\frac {1}{a} + \frac{1}{b} = \frac{1}{c}$

When a = $\frac{4}{5}$ and c = $\frac{2}{3}$

How can i find b?
• Aug 11th 2009, 11:08 AM
earboth
Quote:

Originally Posted by ADY
$\frac {1}{a} + \frac{1}{b} = \frac{1}{c}$

When a = $\frac{4}{5}$ and c = $\frac{2}{3}$

How can i find b?

Plug in the given values:

$\dfrac1{\frac45} + \dfrac1b=\dfrac1{\frac23}$

Move the constants to the RHS of the equation:

$\dfrac1b = \dfrac32 - \dfrac54=\dfrac14$

Thus $b = 4$
• Aug 11th 2009, 11:11 AM
Wilmer
Quote:

Originally Posted by ADY
$\frac {1}{a} + \frac{1}{b} = \frac{1}{c}$

(a + b) / bc = 1 / c
ac + bc = ab
ab - bc = ac
b(a - c) = ac
b = ac / (a - c)

Ya'll ok now ?
• Aug 11th 2009, 11:16 AM
earboth
Quote:

Originally Posted by Wilmer
(a + b) / bc = 1 / c
ac + bc = ab
ab - bc = ac
b(a - c) = ac
b = ac / (a - c)

Ya'll ok now ?

I don't want to pick at you but shouldn't this line

(a + b) / bc = 1 / c