Math Problem Statement
Solution
Let's go through the simplification of the given expression:
Step 1: Factor the Denominator
The common denominator in both fractions is . Let's factor it:
So, we can rewrite the expression as:
Step 2: Combine the Fractions
Since both fractions have the same denominator, we can combine the numerators over the common denominator:
Step 3: Simplify the Numerator
Combine like terms in the numerator:
So we now have:
Step 4: Factor the Numerator if Possible
Notice that has a common factor of 5:
Substitute back into the fraction:
Step 5: Cancel Common Terms
Now, we can cancel from the numerator and the denominator, leaving:
Final Answer
The simplified expression is:
Matching with the Options
This answer matches the third option:
Would you like further explanation or have any questions?
Here are 5 related questions to deepen understanding:
- How would the result change if the numerator was instead of ?
- Why is it helpful to factor both the numerator and denominator before simplifying?
- What would be the domain restrictions for this expression?
- How would you combine terms if the fractions had different denominators?
- What common mistakes should be avoided when simplifying expressions with multiple terms?
Tip: Always look for common factors in the numerator and denominator before canceling to simplify expressions accurately.
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Math Problem Analysis
Mathematical Concepts
Algebra
Rational Expressions
Factoring
Formulas
Factoring trinomials
Combining fractions with common denominators
Theorems
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Suitable Grade Level
Grades 8-10
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