State the restrictions on the variable \(\displaystyle\frac{x+2}{x-3}\)

State the restrictions on the variable \(\displaystyle\frac{5}{x^2-x-6}\)

Reduce \(\displaystyle\frac{x^2-9}{x^2+5x+6}\)

Reduce \(\displaystyle\frac{10a+20}{5a^2-20}\)

Reduce \(\displaystyle\frac{2x^3+2x^2-24x}{x^3+2x^2-8x}\)

Reduce \(\displaystyle\frac{x-5}{x^2-25}\)

A solution of hydrochloric acid (HCl) and water contains \(49\) milliliters of water and \(21\) milliliters of HCl. Find the ratio of HCl to water and of HCl to the total volume of the solution.

The Forest chair lift at the Northstar ski resort in Lake Tahoe is \(5,603\) feet long. If a ride on the lift takes \(11\) minutes, what is the average speed of the lift in feet per minute?

Mini Lecture
Reduce to lowest terms.

1. \(\displaystyle\frac{10a+20}{5a+10}\)

2. \(\displaystyle\frac{x^3+3x^2-4x}{x^3-16x}\)

3. \(\displaystyle\frac{4x^2-12x+9}{4x^2-9}\)