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# 6-5 Operations With Functions

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Simplify. Assume all expressions are defined.

1. (2x+5)-(x2+3x-2)

2. (x-3)(x+1)2

3. (x2-x-6)/(x2-4)

rarinstraw1195  Mar 20, 2017
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1.

(2x + 5) - (x2 + 3x - 2)         Distribute the -1.

(2x + 5) + (-x2 - 3x + 2)       Now we can get rid of the parenthesees.

2x + 5 - x2 - 3x + 2             Combine like terms.

-x2 - x + 7                           Write in descending order.

2.

(x - 3)(x + 1)2                        Write out what the exponent means.

(x - 3)(x + 1)(x + 1)                Multiply each term in each set of parenthesees
(x2 - 2x - 3)(x + 1)                 with each term in every other set.

x3 + x2 - 2x2 - 2x - 3x - 3     Combine like terms.

x3 - x2 - 5x - 3

3.

(x2 - x - 6) / (x2 - 4)                      Factor the numerator and denominator.

[(x - 3)(x + 2)] / [(x - 2)(x + 2)]       The (x + 2)s cancel.

(x - 3) / (x - 2)

hectictar  Mar 20, 2017

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