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P.5 RATIONAL EXPRESSIOS

P.5 RATIONAL EXPRESSIOS. ( التعبير الكسرية ). Objectives:. Simplify Rational Expression Operations on Rational Expressions Determining the LCD of Rational Expressions Complex Fractions. Polynomial – The sum or difference of monomials.

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P.5 RATIONAL EXPRESSIOS

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  1. P.5 RATIONAL EXPRESSIOS (التعبير الكسرية) Objectives: • Simplify Rational Expression • Operations on Rational Expressions • Determining the LCD of Rational Expressions • Complex Fractions

  2. Polynomial – The sum or difference of monomials. • Rational expression – A fraction whose numerator and denominator are polynomials. • Domain of a rational expression – the set of all real numbers except those for which the denominator is zero. • Reduced form – a rational expression in which the numerator and denominator have no factors in common.

  3. Rational Function: Let p(x) and q(x) be polynomials. Then a rational function is given by: The domain (values x can take) of the fcn includes all x-values such that q(x)  0.

  4. Domain= Ex: Find the domain: • The domain of f is all values of x, … but x2 - 4  0; solve by factoring … • (x - 2)(x + 2)  0; • By ZPP, x-2  0; x+2  0 • x   2

  5. solve: x2 + 1  0 x2  -1 No real solutions …. There are no restrictions on the values x can take.

  6. Rational Expressions Operation P, Q, R, and S are polynomials Addition Notice the common denominator Subtraction Find the reciprocal and multiply Multiplication Division

  7. Cancellation Properties

  8. Rational Expressions Cancel common factors Ex: Simplify Factor Cancel common factors Ex: Simplify Factor Multiply Across

  9. Least Common Denominator( LCD) (المقام المشترك الاصغر)

  10. Adding/Subtracting Must have LCD: x(x + 4) Combine like terms Distribute and combine fractions

  11. Complex Fractions ( الكسور المركبة) Multiply by the LCD: x Distribute and reduce to get here Factor to get here

  12. Ex: Simplify

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