If $0.\overline{42}$ is written as a fraction $\frac{a}{b}$ where a and b are positive integers with a greatest common divisor of 1, what is a+b?

Please help asap, tysmmm!

Let x = 0.4242424242....

Then 100x = 42.42424242....

Subtract x from 100x to get 99x = 42

Can you take it from here?

Use the binomial theorem