and
.
x cannot equal 1 or −3 because those values of x would cause the fraction to have a denominator of zero.,
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Factor the numerator and denominator. Cancel the common factor of 2. |
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Factor the numerator and denominator. Cancel the common factor of 5. The result of the division is an integer. We say that the denominator divides evenly into the numerator. |
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The − sign is put either in front of the result
or in front of the numerator; never in front of the denominator.
Reduce the coefficient 6/9 to lowest terms. |
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The two − signs are replaced by a + sign which we don’t have to display.
The coefficient reduces to ¼.
The numerator contains other factors so the 1 in the numerator can be omitted.
Combine the exponentials with base x using the properties of exponents. |
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The − sign is put in front. The coefficient reduces to 1/3.
The identical factors of x 3 in the numerator and denominator cancel.
The numerator contains no other factors so this time the 1 must be displayed.
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After carrying out all the simplifications, the denominator equals 1, so we don’t have to display it. Thus the result is an ordinary expression, not an algebraic fraction. |
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Factor the numerator and denominator. Cancel the common factor of x. |
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Factor the numerator. Cancel the common factor of x − 2. |
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Factor the numerator and factor a − sign out
of the denominator. Cancel the common factor of x − 2. Bring the − sign to the numerator and distribute it. |
Algebra Coach Exercises |