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Chapter 0: Problem 33

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

Short Answer

Expert verified
The combined fraction simplifies to \(2\).

Step by step solution

01

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.
02

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 \(12x + 10\).
03

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 \(\frac{{12x + 10}}{{6x+5}}\).
04

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 \(2\).

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Most popular questions from this chapter

Simplify by reducing the index of the radical. $$\sqrt[4]{7^{2}}$$

Simplify by reducing the index of the radical. $$\sqrt[6]{x^{4}}$$

Exercises will help you prepare for the material covered in the next section. Evaluate each exponential expression in $$ \frac{x^{30}}{x^{-10}} $$

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Describe what it means to raise a number to a power. In your description, include a discussion of the difference between \(-5^{2}\) and \((-5)^{2}\)
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