Answer
$\dfrac{2a - 10}{3a - 5 }$
Restriction: $a \ne \frac{5}{3}$
Work Step by Step
Because both expressions already have a common denominator, we can just simply add the numerators:
$\dfrac{a + 11 + (a - 21)}{3a - 5 }$
Add the terms in the numerator:
$\dfrac{2a - 10}{3a - 5 }$
Now, we need to find the restrictions by seeing what values of the variable will make the denominator equal to zero because if the denominator of any rational expression is zero, the expression is undefined.
To find out the restrictions on the variables, set the denominator equal to zero:
$3a - 5 = 0$
Add $5$ to each side:
$3a = 5$
Divide each side by $3$:
$a = \frac{5}{3}$
Restriction: $a \ne \frac{5}{3}$
