Question

Question 5
For how many integers I is the fraction
41-17
also an integer?
5x +9​

Answer 1

$\frac{4x−17}{5x+9} = \frac{5x+9−x−26}{5x+9} = \frac{5x+9}{5x+9} - \frac{x + 26}{5x + 9} \\ = 1 - \frac{x + 26}{5x + 9} \\ when \: x = - 26 \: \: \: \: \: \: \: \: \: \: \: \: \: \: 1 - \frac{x + 26}{5x + 9} = 1 \\ for \: x = - 26 \: \: \: \: \: \: \: \: \: \frac{4x - 17}{5x + 9} ∈Z$