Math Problem Statement
Simplify the expression: (4x^2 + 4x) / (x^4 + x^3)
Solution
The given expression is:
Step 1: Factor the numerator and the denominator.
-
Numerator:
- Factor out :
-
Denominator:
- Factor out :
Step 2: Simplify the expression.
Now the expression looks like this:
Since appears in both the numerator and the denominator, you can cancel (as long as ):
Step 3: Simplify further.
Now simplify the remaining expression:
So, the simplified expression is:
Final Answer:
The completely simplified expression is .
Do you have any questions or want more details on any of the steps?
Here are 5 related questions to explore further:
- How would the result change if the expression was ?
- What happens if ? Can the expression still be simplified?
- Can you apply the same factoring technique to other polynomial expressions?
- How do you simplify expressions with higher-degree polynomials?
- What other common factorization patterns are useful in simplifying rational expressions?
Tip: Always check for common factors in both the numerator and the denominator when simplifying rational expressions.
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Math Problem Analysis
Mathematical Concepts
Algebra
Simplifying Rational Expressions
Factoring
Formulas
Factoring Polynomials
Cancelling common terms in rational expressions
Theorems
Fundamental Theorem of Algebra
Suitable Grade Level
Grades 8-10