Math Problem Statement
Solution
Let's solve the problem step by step. Here's the given expression:
Step 1: Simplify the numerator
The numerator is . Squaring a negative fraction makes it positive:
Step 2: Simplify the denominator
The denominator involves two terms:
Step 2.1: Simplify
Multiply the fractions:
Step 2.2: Subtract from
Now compute:
To subtract, find a common denominator. The least common denominator of 4 and 8 is 8:
Thus:
The denominator is .
Step 3: Compute the division
Now divide the numerator by the denominator:
Dividing by a fraction is the same as multiplying by its reciprocal:
Multiply the numerators and denominators:
Final Answer:
Would you like further clarifications or explanations?
Follow-Up Questions:
- Can you simplify into a mixed number?
- How do you find the reciprocal of a fraction?
- What is the significance of squaring a fraction like ?
- Can this problem be solved using a calculator, and if so, how do you input fractions?
- What happens if one term in the denominator is zero?
Tip:
Always simplify each component of a complex fraction separately before combining them—it reduces errors!
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Math Problem Analysis
Mathematical Concepts
Arithmetic with Fractions
Order of Operations
Simplifying Expressions
Formulas
Division of Fractions
Multiplication of Fractions
Squaring a Fraction
Theorems
Reciprocal Rule for Division
Suitable Grade Level
Grades 6-8