Simplify. Express your answer as a single fraction in simplest form \[ \frac{t}{t+10}+3 \]

To simplify the expression \( \frac{t}{t+10} + 3 \), we first need to combine the two terms over a common denominator. The common denominator here is \( t + 10 \). Rewrite the number 3 as a fraction: \[ 3 = \frac{3(t+10)}{t+10} \] Now, substitute this into the original expression: \[ \frac{t}{t+10} + \frac{3(t+10)}{t+10} = \frac{t + 3(t + 10)}{t + 10} \] Next, distribute the 3 in the numerator: \[ = \frac{t + 3t + 30}{t + 10} = \frac{4t + 30}{t + 10} \] Now, we can factor out a common factor of 2 in the numerator: \[ = \frac{2(2t + 15)}{t + 10} \] At this point, we check if \( 2t + 15 \) and \( t + 10 \) have any common factors. Since there are none, this is the simplest form of the expression. Therefore, the simplified answer is: \[ \frac{2(2t + 15)}{t + 10} \]