Can you solve this?

$\dfrac{11a + 11b}{a + b} + \dfrac{b}{a + b}$

$11 + \dfrac{1}{\dfrac{a}{b} + 1}$

since $a,b \in N$ , thus when a+b divides it we should get a natural number , now here we can see 1 is not divisible by any natural number rather than 1 . So for the expression to be a natural number , a should be zero, $b \neq 0$ , but $a,b \in N$ .

Thus $\boxed{zero}$ solutions

Here $a+b|11a+12b$ . Now $a+b|11a+11b+b$ We know $a+b|11a+11b$ . Hence $a+b|b$ . But a larger number cannot divide a smaller number. Hence there is no solution.

a must be = 0