Answer
$p=3$
Work Step by Step
Given : $\frac{5p+2}{p} = \frac{17}{p}$
This becomes : $5p+2=17$
(After multiplying both sides of the equation with the least common denominator $p$)
Thus, $5p=17-2=15$
$p=15\div5=3$
Putting $p=3$ in the initial equation,
Left Hand Side, $LHS=\frac{5(3)+2}{2}=\frac{17}{3}$
Right Hand Side, $RHS=\frac{17}{3}$
Hence, $LHS=RHS$