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anemone
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Simplify \(\displaystyle \frac{x^2-4x+3+(x+1)\sqrt{x^2-9}}{x^2+4x+3+(x-1)\sqrt{x^2-9}}\) where \(\displaystyle x>3\).
A rational expression is an algebraic expression that contains one or more fractions with variables in the numerator and/or denominator. It can also be written as a ratio of two polynomial expressions.
To simplify a rational expression, you need to factor the numerator and denominator and then cancel out any common factors. The simplified form of a rational expression is the form that has no common factors in the numerator and denominator.
Simplifying a rational expression involves reducing it to its simplest form, while evaluating a rational expression involves substituting given values for the variables and solving the resulting expression.
The LCD method should be used when the denominators of the fractions in the rational expression are not the same. By finding the LCD and rewriting the fractions with the same denominator, the expression can be simplified further.
Yes, a rational expression can be simplified to a whole number if the numerator is divisible by the denominator with no remainder. However, this is not always the case and the expression may simplify to a fraction instead.