Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{s}{2} + t$

Full solution

Q. Simplify. Express your answer as a single fraction in simplest form.

\newline

\frac{s}{2} + t

Identify Given Expression and Goal: Identify the given expression and the goal. $\newline$ We have the expression $\frac{s}{2} + t$ and we want to express it as a single fraction in simplest form.
Find Common Denominator: Find a common denominator for the terms in the expression. $\newline$ Since $t$ can be written as $t/1$ , we need to find a common denominator for $1/2$ and $1/1$ . The common denominator is $2$ .
Express $t$ with Common Denominator: Express $t$ with the common denominator. $\newline$ To express $t$ with the common denominator of $2$ , we multiply both the numerator and the denominator of $\frac{t}{1}$ by $2$ , which gives us $\frac{2t}{2}$ .
Combine Fractions Over Common Denominator: Combine the fractions over the common denominator. $\newline$ Now we can combine $\frac{s}{2}$ and $\frac{2t}{2}$ into a single fraction: $\newline$ $\left(\frac{s}{2}\right) + \left(\frac{2t}{2}\right) = \frac{s + 2t}{2}$
Check for Further Simplification: Check if the resulting fraction can be simplified further. The fraction $(s + 2t)/2$ is already in simplest form because $s$ and $t$ are variables and we have no information that would allow us to simplify the expression further.