Rational Expressions

Rational Expressions

January 13, 2021

Rational Expressions

A rational expression is a quotient of two polynomial expressions.

 $\frac{x+y}{y+x}=1$    and   $\frac{x-y}{y-x}=-1$  

CAN YOU EXPLAIN WHY??

Operations with Rational Expressions

• Simplifying - Factor then simplify

•  $\frac{64k^3-1}{4k^2-13k+3}$  

•  $\frac{\left(4k-1\right)\left(16k^2+4k+1\right)}{\left(4k-1\right)\left(k-3\right)}$  

•  $\frac{16k^2+4k+1}{k-3}$  

Operations with Rational Expressions

• Multiplying - Factor, then simplify

•  $\frac{x^2-10x-24}{x^3-2x^2}\cdot\frac{5x^2-20x}{x^2-16x+48}$  

•  $\frac{\left(x-12\right)\left(x+2\right)}{x^2\left(x+2\right)}\cdot\frac{5x\left(x-4\right)}{\left(x-12\right)\left(x-4\right)}$  

•  $\frac{5x}{x^2}=\frac{5}{x}$  

Operations with Rational Expressions

• Dividing - Factor, multiply by the reciprocal, then simplify

•  $\frac{2s^2+9s+4}{1-4s^2}\div\frac{2s^2-s-1}{2s^2-3s+1}$  

•  $\frac{\left(2s+1\right)\left(s+4\right)}{\left(1+2s\right)\left(1-2s\right)}\cdot\frac{\left(2s-1\right)\left(s-1\right)}{\left(2s+1\right)\left(s-1\right)}$  

•  $\frac{s+4}{1-2s}=-\frac{s+4}{2s-1}$  

Operations with Rational Expressions

• Adding and Subtracting - Rewrite with a common denominator, combine, then simplify

•  $\frac{3}{4w}-\frac{2}{5w}$  

•  $\frac{5}{5}\cdot\frac{3}{4w}-\frac{2}{5w}\cdot\frac{4}{4}$  

•  $\frac{15-8}{20w}=\frac{7}{20w}$  

Operations with Rational Expressions

• Complex Fractions - Combine the numerator and denominator into a single fraction, multiply by the reciprocal, then simplify