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Simplify completely
x² + 4x - 45/x^2+10x+9
and find the restrictions on the variable.

Sagot :

michellemuniz367

Answer:

(x-5)/(x+1) and x cannot equal -1 because the denominator can't be zero.

Step-by-step explanation:

Factor the numerator:

(x+9)(x-5)

Factor the denominator:

(x+1)(x+9)

So you have

(x+9)(x-5)/(x+1)(x+9); see that you can cross out the (x+9) in both the numerator and denominator?

You're left with (x-5)/(x+1)

The only number that is restricted is -1, because that would make the denominator zero, which is a no no

altavistard

Answer:

Step-by-step explanation:

To avoid ambiguity please write the given expression as  

                                                                 x² + 4x - 45

x² + 4x - 45/(x^2+10x+9) or (better) as ---------------------

                                                                   x^2+10x+9

Notice that both numerator and denominator have the factor x + 9:

 (x + 9)(x - 5)

---------------------

 (x + 9)(x + 1)

This allows us to cancel out the (x + 9) factor, resulting in:

x - 5

------- ONLY for x ≠ -1 and x = -9

x + 1

We must exclude these two x-values because otherwise the denominator would be zero, which is not allowed.

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