Math Problem Statement

Simplify the expression: (1 / (a - b)) + (4 / (b - a)) - (8 / (a + b)) - ((11a - 5b) / (b^2 - a^2))

Solution

The given expression simplifies to 0.

This means the correct answer is the third option: 0\boxed{0}.

Would you like further details on the simplification process or have any other questions?

Here are 5 related questions you might find helpful:

  1. How do you simplify expressions involving fractions with different denominators?
  2. What is the significance of factoring when simplifying algebraic expressions?
  3. How does symmetry in terms like aba - b and bab - a affect simplification?
  4. What techniques can be used to identify common factors in algebraic expressions?
  5. How can you check if two complex expressions are equivalent?

Tip: Always check for possible factorizations in both the numerator and the denominator to simplify complex fractions more easily.

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Math Problem Analysis

Mathematical Concepts

Algebra
Fractions
Factoring
Simplification

Formulas

Difference of squares: b^2 - a^2 = (b - a)(b + a)
Equivalent Fractions: (1 / (a - b)) = (-1 / (b - a))

Theorems

Difference of Squares
Simplifying Rational Expressions

Suitable Grade Level

Grades 10-12