Limit and continuity

Question

 please help me to solve this

Answer 1

\(\lim\limits_{x\to 4} \frac{2x^2 - 4x - 24}{x^2 + 6} - \frac{1}{4 - x}\)

\(=\lim\limits_{x\to 4} \frac{2x^2 - 4x - 24 + x + 4}{x^2 - 16}\)

\(=\lim\limits_{x\to 4} \frac{2x^2 - 3x - 20}{x^2 - 16}\)

\(=\lim\limits_{x\to 4} \frac{(x - 4)(2x + 5)}{(x - 4)(x + 4)}\)

\(=\lim\limits_{x\to 4} \frac{2x + 5}{x + 4}\)

\(=\frac{2 \times 4 + 5}{4 + 4} = \frac{8 + 5}{8} = \frac{13}{8}\)