Help?! Why do we need to factor the numerator and denominator when simplifying rational expressions?
When simplifying a rational expression, why do we need to factor the numerator and the denominator?
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When solving a rational expression, you need to factor the numerator and the denominator in order to cancel out like terms. It is the only way to simplify a rational expression, as you cannot simply cancel out things that look the same like an x^2 or a 2x. You need to verify that the expressions are truly alike by simplifying and then canceling what is exactly the same on the top and the bottom.
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To understand this, think about basic fractions. When you simplify a fraction, you divide the numerator and the denominator by all the factors they have in common.
You can do this by factoring both the numerator and the denominator into prime factors. This allows you to see all the factors there are in common.
The same thing applies to rational expressions. You need to know what is multiplied by what in order to reduce the expression by eliminating the factors that are in common.
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5 years ago
1) 3y/2x 2) (x-3)/(x-1) 3) 3x^2(5x-20x^2+4x+4)
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