Math Problem Statement
Solution
Let's solve the given mathematical expression step by step.
The expression is:
Step 1: Simplify the numerator
The numerator is . Recall that , so rewrite the terms:
Thus, the numerator becomes:
Step 2: Combine the fractions
To combine the fractions, find the least common denominator (LCD), which is . Rewrite the terms with the LCD:
Now subtract the fractions:
Simplify the numerator:
so the combined fraction becomes:
Step 3: Divide by 3
The original expression includes dividing the result by 3. Dividing by 3 is the same as multiplying the denominator by 3:
Simplify:
Final Answer:
The simplified expression is:
Would you like additional clarification or further examples?
Relative Questions:
- How do you combine fractions with different denominators?
- Why is dividing by 3 equivalent to multiplying the denominator by 3?
- What happens if or in this expression?
- Can this expression be expanded further for specific values of ?
- How does this concept relate to simplifying rational expressions?
Tip:
Always check for restrictions in the domain when dealing with fractions to avoid dividing by zero!
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Math Problem Analysis
Mathematical Concepts
Simplification of rational expressions
Negative exponents
Fraction operations
Formulas
x^{-1} = \frac{1}{x}
\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}
Theorems
Basic properties of exponents
Suitable Grade Level
Grades 9-10