Question

select the correct answer.

assuming that no denominator equals zero, what is the simplest form of this expression?

\\\frac{x - 1}{x^2 - 4x + 3} \div \frac{5x - 2}{x^2 - 9}\\

• \\(\frac{x - 1}{x + 3}\\)
• \\(\frac{1}{5x - 2}\\)
• \\(\frac{3}{5x - 2}\\)
• \\(\frac{x + 3}{5x - 2}\\)

Explanation:

Convert division to multiplication by the reciprocal

$$ \frac{x - 1}{x^2 - 4x + 3} \div \frac{5x - 2}{x^2 - 9} = \frac{x - 1}{x^2 - 4x + 3} \cdot \frac{x^2 - 9}{5x - 2} $$

Factor the quadratic expressions

$$
LATEXBLOCK0
$$

Substitute and simplify the expression

$$
LATEXBLOCK1
$$

Answer:

• (A) \(\frac{x - 1}{x + 3}\)
• (B) \(\frac{1}{5x - 2}\)
• (C) \(\frac{3}{5x - 2}\)
• (D) \(\frac{x + 3}{5x - 2}\) (Correct answer)