Math Problem Statement
Determine the sum and difference of each functions. f(x)=\frac{x+5}{x-3}
g(x)=\frac{x+4}{x-2}
Solution
To determine the sum and difference of the functions and , we proceed as follows:
Sum of the Functions
The sum of the functions and is given by:
To add these fractions, we need to find a common denominator, which is .
Now, combine the numerators:
Next, expand the numerators:
Now, add the expanded numerators:
This can be simplified further:
Difference of the Functions
The difference of the functions and is given by:
Again, find a common denominator:
Now, combine the numerators:
Using the previously expanded forms:
Simplify the numerator:
This can be simplified further:
Final Answers:
- Sum of the functions:
- Difference of the functions:
Would you like further details or explanations on any part of this?
Here are some related questions for further exploration:
- What is the product of and ?
- How do you determine the quotient of and ?
- Can you find the domain of ?
- What is the domain of ?
- How would the graphs of and look like?
Tip: Always simplify your expressions as much as possible to make solving and interpreting them easier.
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Math Problem Analysis
Mathematical Concepts
Fractions
Algebra
Function Operations
Formulas
-
Theorems
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Suitable Grade Level
High School
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