Problem 33 - College Algebra Essentials

Question

Add or subtract as indicated. $$\frac{4 x+1}{6 x+5}+\frac{8 x+9}{6 x+5}$$

Step-by-Step Solution

Answer

The simplified result of the addition of the two given fractions is \(\frac{12 x + 10}{6 x + 5}\).

Step 1: Identify fractions with the same denominator

Here both fractions have the same denominator, \(6 x + 5\). Therefore, addition can be carried out by simply combining the numerators.

Step 2: Adding the numerators

Add the numerators of the two fractions, which means: \( (4 x + 1) + (8 x + 9)\). This simplifies to: \(12 x + 10\)

Step 3: Write the final solution

After combining the numerators, place them above the original denominator. So, the solution is \(\frac{12 x + 10}{6 x + 5}\).