Problem 33 - College Algebra

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 combined fraction simplifies to \(2\).

Step 1: Identifying Common Denominator

The common denominator for both fractions is \(6x+5\). This means that both fractions can be directly added or subtracted without the need to find least common multiplier or denominator.

Step 2: Adding the Numerators

Since both fractions share the same denominator, we can add the numerators directly. In this step, \((4x+1)\) and \((8x+9)\) will be added together to yield \(12x + 10\).

Step 3: Constructing the Simplified Fraction

The simplified fraction is formed by placing the sum of the numerators over the common denominator. So, the resulting fraction is \(\frac{{12x + 10}}{{6x+5}}\).

Step 4: Simplifying the Fraction

The fraction can be simplified further by factoring out common factors from the numerator and the denominator. \(\frac{{12x + 10}}{{6x+5}}\) simplifies to \(2\).