How are both integers
Number Theory
Level
5
The sum of absolute values of all real numbers \(x\), such that both of the fractions \(\frac{x^2+4x-1}{7x^2-6x-5}\) and \(\frac{1-x}{1+x}\) are integers, can be written as \( \frac{a}{b} \), where \(a\) and \(b\) are coprime positive integers. What is the value of \(a+b\)?
Details and assumptions
If you think that there are no real numbers \(x\), then the (empty) sum is 0, and you should type your numerical answer as 1.
by
Calvin Lin