Question

lesson 2.5 review - solving rational equations
① \\(\frac{x}{(x + 1)} + \frac{3x + 4}{(x + 1)} = \frac{3}{1}\\) ① factor, lcm (lcd)
multiple-choice question
what does the third fraction need in its denominator in order to have an lcd with the other fractions?
\\(\square\\) \\((x + 1)\\)
\\(\square\\) \\((3x + 4)\\)
\\(\square\\) \\((x + 1)(x + 1)\\)

Explanation:

Step1: Identify denominators

The first two fractions have denominator \( (x + 1) \), and the third fraction has denominator \( 1 \).

Step2: Determine LCD requirement

To find the least common denominator (LCD), we need to make the third fraction's denominator match the common factor of the others. Since the first two have \( (x + 1) \), the third (with denominator \( 1 \)) needs \( (x + 1) \) to have an LCD with \( (x + 1) \) (from the first two) and \( 1 \).

Answer:

\( (x + 1) \) (the option with \( (x + 1) \))