Solve the Simple Equation: 1/d^2 = 1/(81m^2) + 1/(25m^2) in Just a Few Steps!

[superwolf]

How can I solve this equation:

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

?

Try:

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

 

[HallsofIvy]

How can I solve this equation:

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

?

Try:

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

up to here you are fine. But

$$\Rightarrow d^2 = 81m^2 + 25m^2 = 106m^2 \Rightarrow d = 10.3m$$

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.

 

[Mark44]

Or even better, by (25)(81)d²m²