Math Problem Statement
Solution
Let's simplify the expression given in the image step by step. The expression appears to be:
Step 1: Simplify the Numerator
The numerator is .
To subtract these fractions, we need a common denominator. The common denominator between and is . So we rewrite each fraction:
Now, subtract them:
Step 2: Simplify the Denominator
The denominator is .
Again, we need a common denominator, which is . Rewriting each fraction:
Now, subtract them:
Step 3: Form the Overall Fraction
Now we have the expression:
When dividing fractions, we multiply by the reciprocal of the denominator. So we get:
The terms cancel out, leaving us with:
Step 4: Factor the Numerator
The numerator is a difference of squares, which can be factored as:
Final Expression
Now we have:
Notice that is the same as . So, we can cancel out the terms, but we are left with a negative sign:
Thus, the simplified expression is:
Final Answer:
Would you like further details or have any questions?
Here are five questions for further exploration:
- What is the importance of finding a common denominator in fraction operations?
- How can you identify the difference of squares when simplifying expressions?
- Why does canceling terms in a rational expression require factoring first?
- What are the conditions for canceling terms in algebraic fractions?
- How does the negative sign affect the result when simplifying fractions?
Tip: Always check if terms in the numerator or denominator can be factored, as it often simplifies the process of solving.
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Math Problem Analysis
Mathematical Concepts
Algebra
Rational Expressions
Factoring
Difference of Squares
Formulas
Common denominator in fractions: a/b - c/d = (ad - bc)/bd
Difference of squares: x^2 - y^2 = (x - y)(x + y)
Theorems
Difference of Squares
Suitable Grade Level
Grades 9-12
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