Math Problem Statement
Solution
The expression in the image asks to simplify the following equation into a single fraction, with both the numerator and the denominator factored and simplified:
Step 1: Simplify the terms
- The second term is already simplified.
- The third term simplifies to .
Thus, the expression becomes:
Step 2: Express all terms with a common denominator
To combine all terms into a single fraction, the common denominator is . The terms must be rewritten as:
- remains the same.
- Rewrite as .
- Rewrite as .
Thus, the expression becomes:
Step 3: Combine the terms
Now that the terms share the same denominator, combine the numerators:
Final Expression:
The simplified expression in a single fraction is:
If you'd like further details or have any questions, feel free to ask!
Related Questions:
- How do you factor quadratic expressions like ?
- What steps should be taken if the denominator is a binomial instead of a single variable?
- How would you simplify expressions with different denominators?
- Can we apply this method to complex numbers or polynomials with higher degrees?
- How does dividing by zero affect the expression?
Tip:
When simplifying expressions, always look for a common denominator early to reduce the number of operations required later.
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Math Problem Analysis
Mathematical Concepts
Simplification of algebraic fractions
Combining like terms
Factoring
Formulas
a/b + c/b = (a + c)/b
Quadratic expression: ax^2 + bx + c
Theorems
Distributive property of multiplication
Quadratic formula: (-b ± √(b²-4ac)) / 2a
Suitable Grade Level
Grades 10-12
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