What is the simplified form of x plus 1 over x squared plus x minus 6 divided by x squared plus 5x plus 4 over x minus 2?

Answer 1

To simplify the expression (\frac{x + 1}{x^2 + x - 6} \div \frac{x^2 + 5x + 4}{x - 2}), first rewrite it as (\frac{x + 1}{x^2 + x - 6} \cdot \frac{x - 2}{x^2 + 5x + 4}). Next, factor the denominators: (x^2 + x - 6 = (x - 2)(x + 3)) and (x^2 + 5x + 4 = (x + 1)(x + 4)). This results in (\frac{x + 1}{(x - 2)(x + 3)} \cdot \frac{x - 2}{(x + 1)(x + 4)}), allowing cancellation of (x + 1) and (x - 2), leading to the simplified form (\frac{1}{x + 3}) when (x \neq -1, -4, 2).