1) Simplify: \(\Large\frac{x+9-\frac{7x+78}{x+2}}{x-4+\frac{16x+48}{x+2}}\)
2) Simplify: \(\large\frac{x^3+1}{x^2-4x-12}\div\frac{16x^2-16x+16}{8x^2-48x}\)
3) Simplify: \(\large\frac{x^3+2x^2-15x}{x^2-16}\cdot\frac{3x^2-12x}{x^2+3x-10}\)
4) Simplify: \(\Large\frac{\frac{6}{7}+\frac{1}{x}}{\frac{3}{7x}}\)
5) Simplify: \(\large\frac{-3x^2-13x-4}{x^2-4}\div\frac{3x^3+12x^2-x-4}{2-x}\)
6) Simplify: \(\large\frac{x^2+2x-8}{x^3-216}\div\frac{2x^2+8x}{-x^2+9x-18}\div\frac{x^3-2x^2-9x+18}{2x^3+10x^2}\)
7) Simplify: \(\Large\frac{4-\frac{6}{x-3}}{\frac{2}{x}-\frac{1}{x-3}}\)
8) Find the slope of the line through points A \(\left(3,\ \large\frac{k-6}{k+1}\right)\) and B \(\left(1,\ \large\frac{k+4}{k+2}\right)\).
9) When the sum below is written as a simplified rational expression, the difference between the polynomial of the numerator and the polynomials of the denominator is a constant. What is the constant?
\(\large\frac{x}{x+2}-\frac{5}{x+3}-\frac{5}{x^2+5x+6}\)
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