Find the lcd
14/4(x+1) , 7/4x
I don't get it can you please explain step by step?
To find the least common denominator (LCD) for the given fractions, step by step, follow these steps:
Step 1: Identify the denominators of the fractions. In this case, the denominators are 4(x + 1) and 4x.
Step 2: Simplify each denominator (if possible). In this case, the denominators are already in their simplest form.
Step 3: Identify the prime factors of each denominator. A prime factorization is when a number is expressed as the product of prime numbers. Let's factorize the denominators:
- The prime factors of 4(x + 1) are 2, 2, and x + 1.
- The prime factors of 4x are 2, 2, and x.
Step 4: Combine the prime factors from both denominators. When identifying the prime factors, take the highest power for any repeated primes. In this case, we combine the prime factors as follows:
- 2, 2, x + 1, and x.
Step 5: Multiply all the prime factors identified in Step 4 to obtain the LCD. In this case, the LCD is given by:
- (2)(2)(x + 1)(x) = 4x(x + 1).
Therefore, the LCD for the fractions 14/4(x + 1) and 7/4x is 4x(x + 1).