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 Tuesday 27th of February

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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Writing a Rational Expression in Lowest Terms

A rational expression is a fraction where the numerator and the denominator are polynomials. Reducing a rational expression to lowest terms is similar to reducing an arithmetic fraction to lowest terms.

Procedure

To Reduce a Rational Expression to Lowest Terms

Step 1 Factor the numerator and denominator.

Step 2 Cancel pairs of factors that are common to the numerator and denominator.

Example 1

Reduce to lowest terms:

 Solution Step 1 Factor the numerator and denominator. Step 2 Cancel common factors. Simplify.
Thus, the result is

Note:

To factor x2 - 2x - 15:

â€¢ Find two integers whose product is -15 and whose sum is -2. They are 3 and -5.

â€¢ Use these integers to write the factorization (x + 3)(x - 5). To factor x2 - 7x + 10:

â€¢ Find two integers whose product is 10 and whose sum is -7. They are -2 and -5.

â€¢ Use these integers to write the factorization (x - 2)(x - 5).

Example 2

Reduce to lowest terms:

 Solution Step 1 Factor the numerator and denominator. Factor -1 out of the numerator.Notice that in the numerator, -8 + x, can be written as x - 8. Step 2 Cancel common factors. Cancel the common factor of x - 8. Simplify. = -1
So, the fraction reduces to -1.

Note:

Notice that in , the numerator and denominator are opposites. Therefore, reduces to -1.

Example 3

Reduce to lowest terms:
 Solution Step 1 Factor the numerator and denominator. Factor. In the numerator, write 4 - x as -1(x - 4). Step 2 Cancel common factors. Cancel the common factor of x  4. Simplify.
Thus, the fraction reduces to .

Notice that 4 - x can be written as a product where one factor is x - 4: 4 - x = -1(-4 + x) = -1(x - 4)