Question

question #1 determine the least common denominator of the following rational expressions (\frac{4x - 1}{x + 2}) and (\frac{x + 6}{x - 3}) ((x + 2)(x + 3)) ((x - 1)) ((x - 2)(x - 3)) ((x + 2)(x - 3)) question #2 when adding or subtracting rational expressions, the expressions must have a common denominator. false true

Explanation:

Step1: Recall LCD rule for rational expressions

The least - common denominator (LCD) of two rational expressions $\frac{a}{b}$ and $\frac{c}{d}$ is the least common multiple of $b$ and $d$. When $b=x + 2$ and $d=x - 3$, and since $x+2$ and $x - 3$ are distinct linear factors, the LCD is their product.

Step2: Determine the LCD

The LCD of the rational expressions $\frac{4x - 1}{x + 2}$ and $\frac{x+6}{x - 3}$ is $(x + 2)(x - 3)$.

For Question #2:
When adding or subtracting rational expressions $\frac{a}{b}\pm\frac{c}{d}=\frac{ad\pm bc}{bd}$, we need to rewrite the expressions with a common denominator. So the statement "When adding or subtracting rational expressions, the expressions must have a common denominator" is True.

Answer:

Question #1: D. $(x + 2)(x - 3)$
Question #2: True