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Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{t^2u}{4} + \frac{t}{3}$

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Add and subtract rational expressions

Full solution

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

\newline

\frac{t^2u}{4} + \frac{t}{3}

Identify Common Denominator: Identify the common denominator for the fractions $\frac{t^2u}{4}$ and $\frac{t}{3}$ . The common denominator for $4$ and $3$ is $12$ . We need to rewrite both fractions with the common denominator of $12$ .
Rewrite First Fraction: Rewrite the first fraction $t^2u/4$ with the common denominator. $\newline$ To get a denominator of $12$ , we multiply both the numerator and the denominator of $t^2u/4$ by $3$ . $\newline$ $(t^2u/4) \times (3/3) = (3t^2u)/(4\times3) = (3t^2u)/12$
Rewrite Second Fraction: Rewrite the second fraction $\frac{t}{3}$ with the common denominator. $\newline$ To get a denominator of $12$ , we multiply both the numerator and the denominator of $\frac{t}{3}$ by $4$ . $\newline$ $(\frac{t}{3}) \cdot (\frac{4}{4}) = \frac{4t}{3\cdot4} = \frac{4t}{12}$
Add Fractions: Add the two fractions with the common denominator. $\newline$ $(\frac{3t^2u}{12} + \frac{4t}{12} = \frac{3t^2u + 4t}{12})$
Check Simplification: Check if the numerator can be simplified. $\newline$ The numerator $3t^2u + 4t$ cannot be simplified further because there are no common factors other than $1$ .

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