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Illustrating Rational Algebraic Expressions

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Illustrating Rational Algebraic Expressions

  1. 1. Grade 8 – Mathematics Quarter I ILLUSTRATING RATIONAL ALGEBRAIC EXPRESSIONS
  2. 2. 1. illustrate rational algebraic expressions; 2. evaluate rational algebraic expressions, and 3. find every value of the variables that makes a rational expression undefined.
  3. 3. RATIONAL ALGEBRAIC EXPRESSIONS - A rational expression in one variable is an expression that can be written in the form 𝑷 𝑸 , where P and Q are polynomials. 𝟒 𝒙 −𝟐 𝒙 𝟐 + 𝟐𝒙 − 𝟑𝟓 𝟑𝒙 + 𝟒 𝟒𝒙 𝒙 𝟐 + 𝟗 not UNDEFINEDRemember, Q ≠ 0,
  4. 4. EVALUATING ALGEBRAIC EXPRESSIONS Evaluate the expression 𝒙 𝟐− 𝟒 𝒙 −𝟐 when… = 𝒙 𝟐− 𝟒 𝒙 −𝟐 x = 0 = ( ) 𝟐− 𝟒 ( ) −𝟐 0 0 = − 𝟒 −𝟐 = 2 = 𝒙 𝟐− 𝟒 𝒙 −𝟐 x = 1 = ( ) 𝟐− 𝟒 ( ) −𝟐 = − 𝟑 −𝟏 = 3 1 1 = 𝟏− 𝟒 𝟏−𝟐
  5. 5. EVALUATING ALGEBRAIC EXPRESSIONS Evaluate the expression 𝒙 𝟐−𝟐 𝒙 −𝟒 when… = 𝒙 𝟐−𝟐 𝒙 −𝟒 x = 1 = ( ) 𝟐−𝟐 − 𝟒 1 1 = 𝟏−𝟐 𝟏−𝟒 = 𝟏 𝟑 = 𝒙 𝟐− 𝟒 𝒙 −𝟐 x = 2 = ( ) 𝟐−𝟐 −𝟒 = 𝟐 −𝟐 = -1 2 2 = 𝟒 −𝟐 𝟐 − 𝟒 = −𝟏 −𝟑
  6. 6. EVALUATING ALGEBRAIC EXPRESSIONS Evaluate the expression 𝒂 𝟐−𝟐𝒃 𝒂 −𝒃 when… = 𝒂 𝟐−𝟐𝒃 𝒂 −𝒃 a = 1 b = 2 = ( ) 𝟐−𝟐( ) −( ) 1 1 = 𝟏−𝟒 𝟏−𝟐 = 3= −𝟑 −𝟏 2 2 = 𝒂 𝟐−𝟐𝒃 𝒂 −𝒃 a = 2 b = 3 = ( ) 𝟐−𝟐( ) −( ) 2 2 = 𝟒−𝟔 𝟐−𝟑 = 2= −𝟐 −𝟏 3 3
  7. 7. UNDEFINED To make a rational expression 𝒙 𝟐−𝟐 𝒙 −𝟒 UNDEFINED, x – 4 = 0equate the denominator to zero solve for the variable x = 0 + 4 x = 4 The expression 𝒙 𝟐−𝟐 𝒙 −𝟒 is UNDEFINED if x is replaced by 4, because the denominator would be 0.
  8. 8. UNDEFINED To make a rational expression 𝒙 𝟐−𝟒 𝒙 −𝟐 UNDEFINED, x – 2 = 0equate the denominator to zero solve for the variable x = 0 + 2 x = 2 The expression 𝒙 𝟐−𝟒 𝒙 −𝟐 is UNDEFINED if x is replaced by 2, because the denominator would be 0.
  9. 9. UNDEFINED To make a rational expression 𝒙 𝟐−𝒚 𝒙 −𝒚 UNDEFINED, x – y = 0equate the denominator to zero solve for the variable x = 0 + y x = y The expression 𝒙 𝟐−𝒚 𝒙 −𝒚 is UNDEFINED if the variables x and y are replaced by equal values.
  10. 10. Test Yourself. 1. Explain how to evaluate an algebraic expression. 2. What causes a rational expression to be undefined? 3. How do you find the values that may cause a rational expression to be undefined?
  11. 11. Test Yourself. I. Evaluate each rational expression if a = 1 and b = 2 1. 𝑎 𝑏2 2. 2𝑎−𝑏 3𝑎𝑏 II. Find the value of the variable that makes the expression undefined. 1. 3𝑎 4𝑏 2. 2𝑎−𝑏 𝑏−3

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