Math Problem Statement
Find the least common denominator (LCD) of StartFraction 6 x Over x plus 1 EndFraction
and StartFraction 6 Over 7 x plus 7 EndFraction .
Solution
To find the least common denominator (LCD) of two rational expressions, we need to find the least common multiple (LCM) of their denominators.
Given the two expressions:
Step 1: Factor the denominators.
- Denominator of the first expression: (This is already in its simplest form).
- Denominator of the second expression: . We can factor out a 7:
Step 2: Find the least common denominator (LCD).
Now that we have the denominators and , the least common denominator will be the least common multiple of these two denominators. Since the second denominator contains , the LCD is:
Thus, the least common denominator of the two expressions is .
Would you like to explore how to rewrite the fractions with this common denominator or have more details on any step?
Here are 5 related questions:
- How do you simplify rational expressions?
- What is the method to find the LCM of polynomials?
- How do you factor polynomials involving higher degrees?
- Can you convert complex fractions into simpler forms?
- How do you solve rational equations involving different denominators?
Tip: Always factor polynomials to their simplest form before finding the least common denominator!
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Math Problem Analysis
Mathematical Concepts
Algebra
Rational Expressions
Factoring
Formulas
Least Common Multiple (LCM) of denominators
Factoring Polynomials
Theorems
Least Common Denominator
Suitable Grade Level
Grades 8-10
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