Math Problem Statement
A=(x+2/2x-4 - x-2/2x+4 - 8/4-x^2) : 4/x-2 * (x^2-2x+3)
Solution
Let's break down the expression step by step and simplify it:
Given:
Step 1: Simplifying the first part of the numerator
The first three terms in the numerator are:
We can simplify these terms:
- Factor the denominators:
So, the terms become:
Notice that , so the third term becomes:
So, the expression becomes:
Step 2: Combine the terms in the numerator
To combine these terms, let's find a common denominator. The least common denominator (LCD) of , , and is .
Now, rewrite each term with this common denominator:
-
The first term becomes:
-
The second term becomes:
-
The third term remains:
Now combine all the terms:
Step 3: Simplify the numerator
Expand the squares in the numerator: So the numerator becomes: Simplifying:
Thus, the numerator is:
Step 4: Simplify the denominator
The denominator is: Multiply the two terms:
Step 5: Final Expression
Now, combine the numerator and denominator:
To divide by a fraction, multiply by its reciprocal:
Step 6: Simplifying Further
Now, cancel out common terms:
- The terms cancel out, leaving: Simplifying the constants in the denominator:
Finally, factor the numerator:
Cancel out the common terms:
Final Answer:
Let me know if you'd like more details or if you have any questions!
Related questions:
- How can we factor expressions like ?
- What happens when you divide polynomials by fractions?
- Can you explain the process of factoring quadratics in detail?
- What does the concept of least common denominators mean in simplifying rational expressions?
- How does cancellation in fractions work?
Tip: When simplifying complex expressions, break them into smaller steps and carefully factor terms where possible. This helps avoid mistakes and simplifies the process!
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Math Problem Analysis
Mathematical Concepts
Algebra
Rational Expressions
Factoring
Simplification
Formulas
Factoring difference of squares
Simplifying rational expressions
Multiplying and dividing rational expressions
Theorems
Difference of squares theorem
LCD (Least Common Denominator)
Cancellation of common factors in fractions
Suitable Grade Level
Grades 9-12
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