1. ## rational equations

$\displaystyle \frac {1}{a} + \frac{1}{b} = \frac{1}{c}$

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

How can i find b?

$\displaystyle \frac {1}{a} + \frac{1}{b} = \frac{1}{c}$

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

How can i find b?
Plug in the given values:

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

Move the constants to the RHS of the equation:

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

Thus $\displaystyle b = 4$

$\displaystyle \frac {1}{a} + \frac{1}{b} = \frac{1}{c}$
(a + b) / bc = 1 / c
ac + bc = ab
ab - bc = ac
b(a - c) = ac
b = ac / (a - c)

Ya'll ok now ?

4. 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

(a + b) / ab = 1 / c

5. Originally Posted by earboth
I don't want to pick at you but shouldn't this line
(a + b) / bc = 1 / c
(a + b) / ab = 1 / c
Yes, typo...thanks Mr E