Math Problem Statement
Simplify the expression completely if possible. start fraction, 2, x, squared, plus, 16, x, divided by, x, squared, minus, 49, end fraction x 2 −49 2x 2 +16x
Solution
We are tasked with simplifying the expression:
Step 1: Factor the numerator and the denominator.
-
Numerator:
- Factor out the greatest common factor (GCF) of 2x:
-
Denominator:
- This is a difference of squares, and it can be factored as:
Step 2: Substitute the factored forms into the original expression:
Step 3: Simplify the expression.
- There are no common factors between the numerator and the denominator, so the expression is already in its simplest form.
Thus, the simplified expression is:
Would you like to see a detailed breakdown of any part of this solution? Or is there another math topic you'd like to explore?
Here are 5 related questions for further study:
- How would you factor a trinomial like ?
- What are other ways to simplify rational expressions?
- How do you determine when to cancel common factors in rational expressions?
- What are the conditions for division by zero in rational expressions?
- How would you approach simplifying more complex rational expressions involving polynomials of higher degrees?
Tip: Always look for the greatest common factor (GCF) first when factoring expressions, as it can simplify the process significantly.
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Math Problem Analysis
Mathematical Concepts
Algebra
Factoring
Rational Expressions
Difference of Squares
Formulas
Factoring of a trinomial
Difference of squares formula: a^2 - b^2 = (a + b)(a - b)
Theorems
Difference of squares theorem
Factoring trinomials
Suitable Grade Level
Grades 8-10
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