Question

1. \\(\frac{x^2 - 49}{x^2 - 14x + 49} =\\)

\\(\bigcirc\\) 1

\\(\bigcirc\\) 0

\\(\bigcirc\\) \\(\frac{-49}{-14x + 49}\\)

\\(\bigcirc\\) \\(\frac{1}{14x}\\)

\\(\bigcirc\\) \\(\frac{x + 7}{x - 7}\\)

Explanation:

Factor the numerator

$$ x^2 - 49 = (x - 7)(x + 7) $$

Factor the denominator

$$ x^2 - 14x + 49 = (x - 7)^2 $$

Simplify the rational expression

$$ \frac{x^2 - 49}{x^2 - 14x + 49} = \frac{(x - 7)(x + 7)}{(x - 7)(x - 7)} = \frac{x + 7}{x - 7} \quad (x eq 7) $$

Answer:

• 1
• 0
• \(\frac{-49}{-14x + 49}\)
• \(\frac{1}{14x}\)
• \(\frac{x + 7}{x - 7}\) (Correct answer)