20/20 Rational Expressions

A power learning aid combines Guides, Practice and Coaching Calculators to help students master rational expression or rational fraction simplification and rational equation solving.

Rational expression Practice and Coaching Calculators take you step-by-step through the simplification of expressions such as :

(6x³ + 7x² - 1)/(2x² + 3x + 1)
(x² + 6x + 8)/(x + 2)
(x² - 5x + 6)/(14 + 3x - 5x²)
(3x - 9)/(6x - 12)

Detailed steps :

- Factoring out numeric or algebraic factors
- Factoring linear numerators/denominators
- Factoring quadratic numerators/denominators
- Factoring cubic numerators/denominators
- Dividing out or canceling common factors

Rational equation Practice takes you step-by-step through the solving of equations such as :

(5x + 3)/4 + (1 + 3x)/5 = 4/5
2/(3x²) + 5/x = 3/(4x)
1/(3x + 6) - 3/(5x² + 8x - 4) = -5/(15x - 6)
(2x - 1)/(3x + 2) - (1 - x)/(6x² + 7x - 2) = 7/20

Detailed steps :

- Factoring denominators
- Finding Least Common Denominator (LCD)
- Multiplying through by LCD or making each term have LCD
- Solving resulting linear or quadratic equation

The Guide also covers the addition and subtraction of rational expressions such as

3/(x + 1) + 2x/(x² - 6x - 7)

and the multiplication and division of rational expressions such as

(x² - 1)/(9x² - 1) * (6x + 2)/(3x² - 3x).