Add the following.
[tex]\frac{11 x+17}{3 x+5}+\frac{x+3}{3 x+5}[/tex]
Answer (1)
Add the numerators: ( 11 x + 17 ) + ( x + 3 ) .
Combine like terms in the numerator: 12 x + 20 .
Write the result as a single rational expression: 3 x + 5 12 x + 20 .
Simplify the rational expression by factoring out a 4 from the numerator: 3 x + 5 4 ( 3 x + 5 ) .
Cancel the common factor of ( 3 x + 5 ) : 4 .
The final answer is 4 .
Explanation
Understanding the Problem We are asked to add two rational expressions.
Common Denominator The two rational expressions have the same denominator, 3 x + 5 .
Simplification We need to simplify the result.
Examples
Rational expressions are used in various fields, such as physics and engineering, to model relationships between different quantities. For example, in electrical engineering, rational functions can describe the impedance of a circuit as a function of frequency. Simplifying these expressions helps engineers analyze and design circuits more efficiently. Understanding how to add and simplify rational expressions provides a foundation for solving more complex problems in these fields.
