give me example of rational algebraic expression
Answer (1)
Rational Algebraic Expressions1.) Simplify [tex]$\large\sf{\frac{6x}{9x^2}}$[/tex]Solution Process:Factor out common factors in the numerator and the denominator.[tex]$\sf{6x = 3 \cdot 2 \cdot x}$[/tex][tex]$\sf{9x^2 = 3 \cdot 3 \cdot x \cdot x}$[/tex][tex]$\sf{\frac{6x}{9x^2} = \frac{3 \cdot 2 \cdot x}{3 \cdot 3 \cdot x \cdot x} = \frac{2}{3x}}$[/tex]Final answer: [tex]$\sf{\frac{2}{3x}}$[/tex]___________________________2.) Simplify [tex]$\sf{\frac{x^2 - 25}{x^2 + 5x}}$[/tex]Solution Process:Factor the numerator and the denominator.Numerator: [tex]$\sf{x^2 - 25}$[/tex] is a difference of squares, so [tex]$\sf{x^2 - 25 = (x - 5)(x + 5)}$[/tex]Denominator: [tex]$\sf{x^2 + 5x = x(x + 5)}$[/tex][tex]$\sf{\frac{x^2 - 25}{x^2 + 5x} = \frac{(x - 5)(x + 5)}{x(x + 5)} = \frac{x - 5}{x}}$[/tex]Final answer: [tex]$\sf{\frac{x-5}{x}}$[/tex]___________________________3.) Simplify [tex]$\sf{\frac{3x}{x+4} + \frac{5}{x+4}}$[/tex]Solution Process:Since the denominators are the same, add the numerators.[tex]$\sf{\frac{3x}{x+4} + \frac{5}{x+4} = \frac{3x + 5}{x+4}}$[/tex]Final answer: [tex]$\sf{\frac{3x+5}{x+4}}$[/tex]
