Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 5: Practice 1

Write the following expression in the simplest form. State any restriction(s) on the variable.

$\frac{(a-b)(a+2b)}{(a-2b)(b-a)}$.

Write the following expression in the simplest form. State any restriction(s) on the variable.

$\frac{x^2+6x+8}{x^2+7x+10}$.

Write the following expression in the simplest form. State any restriction(s) on the variable.

$\frac{x^2+x-12}{x^2-x-6}$.

Write the following expression in the simplest form. State any restriction(s) on the variable.

$\frac{x^2-3x-10}{x^2+2x-35}$.

Write the following expression in the simplest form. State any restriction(s) on the variable.

$\frac{x^3-12x^2+32x}{x^2-7x+12}$.

Write the following expression in the simplest form. State any restriction(s) on the variable.

$\frac{x^2-4x-21}{x^2-3x-18}$.

Write an unsimplified rational expression in $x$ that has a quadratic expression in the numerator and the restriction on $x$ that $x\notin \{-2,5\}$.

Write a rational expression in $x$ which simplifies to $\frac{x+3}{x-10}$, and where $x\notin \{6,10\}$.