Questions: Add. [ -frac2 s+2 t13 s+frac5 s+3 t13 s ] Simplify your answer as much as possible.

$Add. [ -frac2 s+2 t13 s+frac5 s+3 t13 s ] Simplify your answer as much as possible.$

Transcript text: Add. \[ -\frac{2 s+2 t}{13 s}+\frac{5 s+3 t}{13 s} \] Simplify your answer as much as possible. Answer: $\square$

Solution

Solution Steps

Step 1: Combine the fractions

Since both fractions have the same denominator $13s$, we can combine them directly: \[ -\frac{2s + 2t}{13s} + \frac{5s + 3t}{13s} = \frac{-(2s + 2t) + (5s + 3t)}{13s}. \]

Step 2: Simplify the numerator

Distribute the negative sign and combine like terms in the numerator: \[ -(2s + 2t) + (5s + 3t) = -2s - 2t + 5s + 3t = (5s - 2s) + (3t - 2t) = 3s + t. \]

Step 3: Write the simplified fraction

Substitute the simplified numerator back into the fraction: \[ \frac{3s + t}{13s}. \]