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# Simplifying Rational Algebraic Expressions

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### Simplifying Rational Algebraic Expressions

1. 1. Grade 8 – Mathematics Quarter I SIMPLIFYING RATIONAL ALGEBRAIC EXPRESSIONS
2. 2. 1. illustrate rational algebraic expressions; and 2. simplify rational algebraic expressions.
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. DOMAIN - is the set of all possible values of the variable that are allowed. - restricted values can make a rational expression undefined.
5. 5. 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 Domain: All real numbers except 4.
6. 6. UNDEFINED To make a rational expression 𝟐𝒙 (𝒙 𝟐+𝟓𝒙+𝟔) UNDEFINED 𝒙 𝟐 + 𝟓𝒙 + 𝟔equate the denominator to zero solve for the variable Domain: All real numbers except -2 and -3. (x + 2)(x + 3) = 0 x + 2 = 0 x + 3 = 0 x = -2 x = -3
7. 7. UNDEFINED To make a rational expression 𝟐𝒙 (𝒙 𝟐−𝟗) UNDEFINED, 𝒙 𝟐 − 9 = 0equate the denominator to zero solve for the variable x + 9 = 0 Domain: All real numbers except -9 and 9. (x + 9)(x -9) = 0 x - 9 = 0 x = - 9 x = 9
8. 8. SIMPLIFYING RATIONAL ALGEBRAIC EXPRESSIONS Factor the numerator and denominator Example: 𝟔𝒙+𝟏𝟐 𝟑 = 𝟑(𝟐𝒙+𝟔) 𝟑 Cancel out or divide the common factor. = 𝟑(𝟐𝒙+𝟔) 𝟑 Simplify. = 2x + 6 GCF: 3
9. 9. SIMPLIFYING RATIONAL ALGEBRAIC EXPRESSIONS Factor the numerator and denominator Example: 𝒙 𝟐−𝟔𝒙+𝟖 𝟒𝒙−𝟖 = (𝒙−𝟒)(𝒙−𝟐) 𝟒(𝒙−𝟐) Cancel out or divide the common factor. = (𝒙−𝟒)(𝒙−𝟐) 𝟒(𝒙−𝟐) Simplify. = (𝒙−𝟒) 𝟒 GCF: 4
10. 10. SIMPLIFYING RATIONAL ALGEBRAIC EXPRESSIONS Factor the numerator and denominator Example: 𝒂 𝟐+𝒂−𝟔 𝒂 𝟐−𝟐𝒂−𝟏𝟓 = (𝒂+𝟑)(𝒂−𝟐) (𝒂−𝟓)(𝒂+𝟑) Cancel out or divide the common factor. = (𝒂+𝟑)(𝒂−𝟐) (𝒂−𝟓)(𝒂+𝟑) Simplify. = (𝒂−𝟐) (𝒂−𝟓)
11. 11. SIMPLIFYING RATIONAL ALGEBRAIC EXPRESSIONS Factor the numerator and denominator Example: 𝟑𝒙 𝟐 𝒚 𝟒 𝟗𝒙 𝟑 𝒚 𝟐 = 𝟑·𝒙 𝟐·𝒚 𝟐·𝒚 𝟐 𝟗·𝒙 𝟐·𝒙·𝒚 𝟐 Cancel out or divide the common factor. = 𝟑·𝒙 𝟐·𝒚 𝟐·𝒚 𝟐 𝟗·𝒙 𝟐·𝒙·𝒚 𝟐 Simplify. = 𝒚 𝟐 𝟑𝒙
12. 12. SIMPLIFYING RATIONAL ALGEBRAIC EXPRESSIONS Factor the numerator and denominator Example: 𝟏𝟐𝒙 𝟓 𝒚 𝟒 𝟐𝒙 𝟑 𝒚 𝟕 = 𝟏𝟐·𝒙 𝟑·𝒙 𝟐·𝒚 𝟒 𝟐·𝒙 𝟑·𝒚 𝟒·𝒚 𝟑 Cancel out or divide the common factor. = 𝟏𝟐·𝒙 𝟑·𝒙 𝟐·𝒚 𝟒 𝟐·𝒙 𝟑·𝒚 𝟒·𝒚 𝟑 Simplify. = 𝟔𝒙 𝟐 𝒚 𝟑