Top and bottom

Learning Objectives Define a rational expression and identify its 'top' (numerator) and 'bottom' (denominator). Determine the non-permissible values of a rational expression by setting the 'bottom' (denominator) equal to zero. Simplify rational expressions by factoring both the 'top' and 'bottom' and cancelling common factors. Multiply and divide rational expressions. Add and subtract rational expressions by finding a least common 'bottom' (denominator). Solve simple rational equations. Ever wondered what happens when a simple fraction gets a major upgrade with variables and quadratics? 🤯 Let's explore the world of 'top and bottom' math! In this tutorial, we'll explore rational expressions, whi...

TermDefinitionExample Rational ExpressionA fraction where the 'top' (numerator) and 'bottom' (denominator) are both polynomials. The value of the polynomial in the denominator cannot be zero.(x^2 + 2x + 1) / (x - 3) Numerator ('Top')The polynomial expression written above the fraction bar.In the expression (x + 5) / (x - 2), the numerator is (x + 5). Denominator ('Bottom')The polynomial expression written below the fraction bar.In the expression (x + 5) / (x - 2), the denominator is (x - 2). Non-Permissible Values (NPVs)Any value for a variable that makes the denominator ('bottom') of a rational expression equal to zero. These values are excluded from the domain.For (x + 5) / (x - 2), the NPV is x = 2, because it would make the bottom zero...

The Fundamental Rule of Top and Bottom \frac{P(x) \cdot K(x)}{Q(x) \cdot K(x)} = \frac{P(x)}{Q(x)} This rule allows us to simplify rational expressions. If the 'top' and 'bottom' share a common polynomial factor, K(x), it can be cancelled out, provided K(x) is not zero. Multiplication Rule \frac{A}{B} \cdot \frac{C}{D} = \frac{A \cdot C}{B \cdot D} To multiply rational expressions, multiply the 'tops' together and multiply the 'bottoms' together. Always simplify the result. Division Rule \frac{A}{B} \div \frac{C}{D} = \frac{A}{B} \cdot \frac{D}{C} = \frac{A \cdot D}{B \cdot C} To divide rational expressions, multiply the first expression by the reciprocal of the second. This means you 'flip' the 'top' and &#...