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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:
If α, β are the zeros of the polynomial x 2 +8x +6 frame a Quadratic polynomial whose zeros are a) 1/α and 1/β b) 1+ β/α , 1+ α/β. Ans. P(x) = x 2 +8x +6 α + β = -8
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