Simplifying rational expressions and restrictions

Lessons

• Introduction
  Why is it important to determine the non-permissible values prior to simplifying a rational expression?

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• 1.
  For each rational expression:
  i) determine the non-permissible values of the variable, then
  ii) simplify the rational expression
  a)

  $\frac{{6{x^3}}}{{4x}}$
  
  
  b)

  $\frac{{5 - {x}}}{{{x^2} - 8x + 15}}$
  
  
  c)

  $\frac{{{x^2} + 13x + 40}}{{{x^2} - 25}}$
  
  

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• 2.
  For each rational expression:
  i) determine the non-permissible values of the variable, then
  ii) simplify the rational expression
  a)

  $\frac{{9{t^3} - 16t}}{{3{t^2} + 4t}}$
  
  
  b)

  $\frac{{{x^2} + 2x - 3}}{{{x^4} - 10{x^2} + 9}}$
  
  

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• 3.
  For each rational expression:
  i) determine the non-permissible values of the variable, then
  ii) simplify the rational expression
  a)

  $\frac{{x - 3}}{{3 - x}}$
  
  
  b)

  $\frac{{5{y^3} - 10{y^2}}}{{30 - 15y}}$
  
  
  c)

  $\frac{{1 - 9{x^2}}}{{6{x^2} - 7x - 3}}$
  
  

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• 4.
  The area of a rectangular window can be expressed as $4{x^2} + 13x + 3$, while its length can be expressed as $4x + 1$.
  a)

  Find the width of the window.
  
  
  b)

  If the perimeter of the window is 68 $m$, what is the value of $x$?
  
  
  c)

  If a cleaning company charges $3/$m^2$ for cleaning the window, how much does it cost to clean the window?
  
  

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• 5.
  For each rational expression:
  i) determine the non-permissible values for $y$ in terms of $x$ , then
  ii) simplify, where possible.
  a)

  $\frac{{2x + y}}{{2x - y}}$
  
  
  b)

  $\frac{{x - 3y}}{{{x^2} - 9{y^2}}}$
  
  

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