| RATIONAL FUNCTIONS |
| Rational functions are those which contain a numerator and denominator, and the denominator must not equal 0. |
| A rational function is one in which one term is divided by another. Examples of rational functions: x+2 Can not be simplified. Can also be represented as (x+2)(x-5)^ -1 x-5 x^2 -5x + 6 = (x-2)(x-3) = x-2 x-3 x-3 Always try to factor the numerator first and then simplify, if possible. Let's try something more complex: (x+5)(x-4)(x+3) = x + 5 Two terms cancel each other out. (x-4)(x+3) Let's go one step further: x+2 + x-5 = (x+2)(x-6) + (x+7)(x-5) = x^2 -4x -12 + x^2+2x-35 x+7 x-6 (x+7)(x-6) x^2 +x-42 = 2x^2 -2x - 47 x^2+x-42 Sometimes the solution is not so simple. One more example: x+1 - x-1 + 3 = 7(x+1)-4(x-1) + 1.5 4 7 2 28 7x+7-4x+4 + 1.5 28 7x +7 -4x+4 +(28)(1.5) 28 = 3x +53 28 Another example: 2x + 9x + 3x = 14x = 2x 7 7 7 7 |
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