# Simple equation

1. Mar 12, 2009

### superwolf

How can I solve this equation:

$$\frac{1}{d^2} = \frac{1}{(9m)^2} + \frac{1}{(5m)^2}$$

?

Try:

$$\frac{1}{d^2} = \frac{1}{81m^2} + \frac{1}{25m^2} \Rightarrow d^2 = 81m^2 + 25m^2 = 106m^2 \Rightarrow d = 10.3m$$

2. Mar 12, 2009

### HallsofIvy

Staff Emeritus
up to here you are fine. But
is not true. if
$$\frac{1}{a}= \frac{1}{b}+ \frac{1}{c}$$
it is NOT true that a= b+ c.
More specifically,
$$\frac{1}{\frac{1}{b}+ \frac{1}{c}}\ne b+ c$$

I recommend that you multiply both sides of the equation by the least common divisor of all three fractions, (25)(81)d2.

Last edited: Mar 12, 2009
3. Mar 12, 2009

### Staff: Mentor

Or even better, by (25)(81)d2m2