Algebraic Fraction

Algebraic Fraction

An algebraic fraction is a fraction where the numerator, the denominator, or both contain algebraic expressions (terms with variables). They follow the same rules as regular fractions but involve variables like $x$, $y$, $a$, or $b$. 

Key Points on Algebraic Fraction: 

1. The numerator and/or denominator include variables. 

2. The denominator cannot be zero (e.g., in $\frac{1}{x}$, $x\ne 0$). 

3. They can often be simplified by factoring or canceling common terms. 

Examples of Algebraic Fration: 

1. Simple Algebraic Fraction: 

   $\frac{2x+5}{3}$ 

   Explanation: The numerator $2x+5$ is an algebraic expression, while the denominator is a number. 

2. Fraction with Variable in Denominator: 

   $\frac{7}{y-2}$ 

   Explanation: The denominator $y-2$ is an algebraic expression. Here, $y\ne 2$ (since division by zero is undefined). 

3. Simplifiable Algebraic Fraction: 

   $\frac{x^2-9}{x+3}$ 

   Simplification: Factor the numerator: 

   $\frac{(x-3)(x+3)}{(x+3)}$. Cancel $x+3$ (if $x\ne -3$): 

   Simplified form: $x-3$.