“Simplify” each of these rational expressions by removing any common factors from the numerator and denominator. You can check your answer by testing the initial expression and your result at some simple values of the variables to ensure they’re equal.
\(\displaystyle \frac{x^5-5x^3-7x^2}{x^2} \)
\(\displaystyle \frac{x^3-3x^2}{x-3} \)
\(\displaystyle \frac{x^3-x^2-6}{x+2} \)
\(\displaystyle \frac{x^2-9}{(x-3)^2} \)
\(\displaystyle \frac{x^2+4x-5}{x-1} \)
\(\displaystyle \frac{x^2+18x+77}{x^2+17x+66} \)
\(\displaystyle \frac{x^2-10x-24}{x^2-x-6} \)
\(\displaystyle \frac{x^2-1}{x^3-1} \)
\(\displaystyle \frac{x^2+11x+24}{x^2+5x-24} \)
\(\displaystyle \frac{x^2-7x-44}{x^2+x-20} \)
\(\displaystyle \frac{21-4x-x^2}{56+15x+x^2} \)
\(\displaystyle \frac{\bigl(x^2-4x+4\bigr)(x-1)}{x^2-3x+2} \)
\(\displaystyle \frac{(x+5)^3}{x^2+10x+25} \)
\(\displaystyle \frac{x^3-x^2}{x^2+4x-5} \)
\(\displaystyle \frac{4x+x^2}{x^3+6x^2+8x} \)
\(\displaystyle \frac{x^3-2x^2-2x-3}{x-3} \)
\(\displaystyle \frac{2x-1}{2x^3+15x^2+4x-6} \)
\(\displaystyle \frac{x^3+3x^2-11x-5}{x^2-2x-1} \)