Let's Start Thinking


Slide Notes

Glossary

All Slides

 

Multiplying and Dividing Rational Expressions

Multiplying and Dividing Rational Expressions

Previously, we learned about restrictions and simplifying a single rational expression.

\(\dfrac{4x^3y}{16x^2y^4}\)

\(=\dfrac{4\times x\times x\times x\times y}{4\times 4\times x\times x\times y\times y\times y\times y},~ x \ne 0,~ y \ne 0\)

 

\(=\dfrac{4}{4}\times \dfrac{\cancel{x}}{\cancel{x}}\times \dfrac{\cancel{x}}{\cancel{x}}\times \dfrac{\cancel{y}}{\cancel{y}}\times \dfrac{x}{4\times y\times y\times y}\)

 

\(=1\times 1\times 1\times 1\times \dfrac{x}{4y^3}\)

 

\(=\dfrac{x}{4y^3}\)

Paused Finished
Slide /

Lesson Goals

  • Multiply and divide rational expressions.
  • Simplify these expressions and state restrictions on the variable values.

Try This

Given the simple interest formula, \(I=Prt\), determine a simplified expression for the interest earned when \($\left(\dfrac{2x^2+4x+2}{x^2-1}\right)\) is invested for  \(\dfrac{3x^2+2x-5}{2x^2-4x-6}\) years at \(\left(\dfrac{100}{3x+5}\right)\%\) for \(x\gt3\).

The simple interest formula is  \(I=Prt\), where

  • \(I\) represents interest earned, in dollars,
  • \(P\) is the principal (the amount invested), in dollars,
  • \(r\) is the annual interest rate (expressed as a decimal), and
  • \(t\) is the time in years.