Math Problem Statement
Simplify the rationalize expression.
Solution
To simplify the given rational expression:
we should first factor both the numerator and the denominator.
Step 1: Factor the numerator
The numerator is . We need to find two numbers that multiply to (the constant term) and add to (the coefficient of the middle term).
These numbers are and . Therefore, we can factor the numerator as:
Step 2: Factor the denominator
The denominator is . We need to find two numbers that multiply to (the constant term) and add to (the coefficient of the middle term).
These numbers are and . Therefore, we can factor the denominator as:
Step 3: Simplify the expression
Now, substitute the factored forms back into the original expression:
We can cancel the common factor in both the numerator and the denominator, as long as .
Thus, the simplified expression is:
Final Answer:
The simplified rational expression is , with the restriction that (to prevent division by zero in the original expression).
Would you like further details or have any questions? Here are some related problems you might find interesting:
- Simplify .
- Factor and simplify .
- Solve for in the equation .
- Simplify the expression .
- Determine the values of for which is undefined.
Tip: When simplifying rational expressions, always check for common factors in the numerator and denominator, and don't forget to state any restrictions on the variable that arise from the original expression.
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Math Problem Analysis
Mathematical Concepts
Rational Expressions
Factoring
Formulas
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Theorems
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Suitable Grade Level
Grades 9-12
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