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Lesson 39

Lesson 39. Using the distributive property to simplify rational expressions. Rational expression. A rational expression is an expression with a variable in the denominator.

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Lesson 39

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  1. Lesson 39 Using the distributive property to simplify rational expressions

  2. Rational expression • A rational expression is an expression with a variable in the denominator. • They can be treated just like fractions, so the denominator cannot equal 0. Therefore any value for the variable that makes the denominator 0 is not permitted. • We often use the distributive property to simplify rational expressions.

  3. simplify • x2 ( x2 + 3y3) = x4 + 3x2y3 = x4 + 3x2 y • y2 y m y3 y2m y3 m • What values would make the denominators 0?

  4. simplify • a ( a2 + 3b2 ) • b3 b z

  5. Simplifying with subtraction • m ( axp – 2m4p4 ) • z mk • maxp -2 m5p4 • zmk • axp - 2m5p4 • zk • What values can the variables not be?

  6. simplify • x2 ( dmy - 2x3y ) • c2 x2a

  7. Simplifying with negative exponents • b3 ( 2b2 – f-3d ) • d-3 d b • You can simplify this exactly the same way you did previous examples, but remember to make all exponents positive at the end. • Or • You can move the negative exponents first, and then distribute

  8. simplify • n-1 ( mx + 5n-4p-5 ) • m cn-3p-5 • x2 ( x2 - 3z-2y ) • y-3 y x

  9. Distributing over multiple operations • ab(axb + 2bx - 4 ) • c2 c c2 • ab(axb) + ab(2bx) +ab(-4) • c2(c) c2 c2(c2) • a2b2x + 2ab2x - 4ab • c3 c2 c4

  10. simplify • mn-4 ( m-2rn - n4r-2 + 8m ) • p-2 p3 p

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