Math Problem Statement
Solution
The given expression is:
To divide this expression, we need to factor the numerator and simplify if possible.
Step 1: Factor the numerator .
We are looking for two numbers that multiply to (the constant term) and add to (the coefficient of the linear term). The numbers that satisfy this are and , because:
Thus, the factored form of the numerator is:
Step 2: Simplify the expression.
Now substitute the factored form into the original expression:
Cancel the common factor from both the numerator and denominator (assuming to avoid division by zero):
Final Answer:
The simplified expression is:
Would you like further details or have any questions?
Here are 5 related questions:
- How do you factor quadratic expressions?
- What happens if there is no common factor in such division problems?
- How can you verify if your factored form is correct?
- What is the condition for cancelling terms in rational expressions?
- Can you use synthetic division for such problems? When would that be appropriate?
Tip: Always check for restrictions in the variable when cancelling terms in rational expressions (like ensuring the denominator is not zero).
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Polynomial Division
Factoring Quadratics
Formulas
Factoring a quadratic expression: (a^2 + bx + c) = (a + p)(a + q)
Theorems
Factoring Theorem
Cancellation in Rational Expressions
Suitable Grade Level
Grades 8-10
Related Recommendation
Polynomial Division of (-8a^2 - 31a^3 + a^2 + 15a + 4) by (8a^2 + 7a + 2)
Divide Polynomial (x² + 12x + 27) by (x + 9)
Polynomial Long Division: Dividing (4x^2 − 9x − 9) by (4x + 3)
Simplify Polynomial Division: (x^4 + 2x^3 - 8x^2 + 18x - 9) / (x^2 - 9)
Polynomial Division: Dividing -a^3 + 25a by (a - 5)