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Explain Simplifying Rational Expressions ?
A rational expression, or algebraic fraction, is an expression in which you have a polynomial divided by a polynomial. Sometimes it is said that a rational expression is a polynomial "over" a polynomial.
Here are two examples of rational expressions:
10x3y/15x2y4 and (2x2 +11x +15) /x2-9
Important: The bottom polynomial can never be zero, because division by zero is undefined!To simplify or reduce a fraction such as 6/15, you must first factor the numerator and denominator, and then you can eliminate, or cross out, the common factors.
Like this:
The same canceling procedure can be used to simplify rational expressions. Here are some examples of how you can do this:
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Example Multiply 3x 5 + 4x 3 + 2x - 1 and x 4 + 2x 2 + 4. The product is given by 3x 5 . (x 4 + 2x 2 + 4) + 4x 3 . (x 4 + 2x 2 + 4) + 2x .
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