M3 Multiplying And Dividing Rational Expressions Part 1

M3 Multiplying And Dividing Rational Expressions Part 1 Youtube To identify a rational expression, factor the numerator and denominator into their prime factors and cancel out any common factors that you find. if you are left with a fraction with polynomial expressions in the numerator and denominator, then the original expression is a rational expression. if not, then it is not a rational expression. Multiplying and dividing rational expressions part 1.

Multiply And Dividing Rational Expressions After multiplying rational expressions, factor both the numerator and denominator and then cancel common factors. make note of the restrictions to the domain. the values that give a value of 0 in the denominator are the restrictions. to divide rational expressions, multiply by the reciprocal of the divisor. the restrictions to the domain of a. To divide rational functions, we divide the resulting rational expressions on the right side of the equation using the same techniques we used to divide rational expressions. example 7.12 find r ( x ) = f ( x ) g ( x ) r ( x ) = f ( x ) g ( x ) where f ( x ) = 3 x 2 x 2 − 4 x f ( x ) = 3 x 2 x 2 − 4 x and g ( x ) = 9 x 2 − 45 x x 2 − 7. Definition 5.1.1. a rational expression is an expression of the form p q, where p and q are polynomials and q ≠ 0. here are some examples of rational expressions: − 24 56 5x 12y 4x 1 x2 − 9 4x2 3x − 1 2x − 8. notice that the first rational expression listed above, − 24 56, is just a fraction. since a constant is a polynomial. Divide rational expressions. to divide rational expressions we multiply the first fraction by the reciprocal of the second, just like we did for numerical fractions. remember, the reciprocal of a b a b is b a b a. to find the reciprocal we simply put the numerator in the denominator and the denominator in the numerator. we “flip” the fraction.

Multiplying And Dividing Rational Expressions Definition 5.1.1. a rational expression is an expression of the form p q, where p and q are polynomials and q ≠ 0. here are some examples of rational expressions: − 24 56 5x 12y 4x 1 x2 − 9 4x2 3x − 1 2x − 8. notice that the first rational expression listed above, − 24 56, is just a fraction. since a constant is a polynomial. Divide rational expressions. to divide rational expressions we multiply the first fraction by the reciprocal of the second, just like we did for numerical fractions. remember, the reciprocal of a b a b is b a b a. to find the reciprocal we simply put the numerator in the denominator and the denominator in the numerator. we “flip” the fraction. Multiplication. to multiply a rational expression: 1. factor all numerators and denominators. 2. cancel all common factors. 3. either multiply the denominators and numerators together or leave the solution in factored form. Dividing rational expressions. division of rational expressions works the same way as division of other fractions. to divide a rational expression by another rational expression, multiply the first expression by the reciprocal of the second. using this approach, we would rewrite \frac {1} {x}\div \frac { {x}^ {2}} {3} x1 ÷ 3x2 as the product.