Posted by **Sarah** on Tuesday, December 8, 2009 at 6:28pm.

Simplify each expression.

1. 2x+8/x^2-16

2. 1+x/x^2+x

3. x^2-12x-28/x^2-14x

4. x^2+7x+10/x^2-4

- Math -
**Reiny**, Tuesday, December 8, 2009 at 7:27pm
You probably meant

1. (2x+8)/(x^2-16)

then this factors to

2(x+4)/[(x+4)(x-4)]

= 2/(x-4), where x is not equal to -4

With the proper use of brackets, the others factor as well.

Let me know how you made out with them.

- Math -
**Sarah**, Tuesday, December 8, 2009 at 7:36pm
Thank you so much.

1. (x^2-12x-28)/(x^2-14x)

Answer: (x+2)/(x)

2. (x^2+7x+10)/(x^2-4)

Answer: (x+5)/(x-2)

3. (y^2-16)/(y^2-7y+12)

Answer: (y+4)/(y-3)

Could you check my answers for these questions. I will really appeciate it. Thank you so much again.

- Math -
**Reiny**, Tuesday, December 8, 2009 at 7:52pm
Your answers are all correct.

Have you learned about restrictions?

e.g. in the first one you probably had

(x-14)(x+2)/[(x(x-14)] , then canceled the x-14.

but suppose x = 14. Didn't you just divide by zero ?

That is why we have to exclude the value of the variable which would have made that denominator zero.

so the complete answer to that one would have been ...

(x+2)/x , x not equal to 14

- Math -
**Sarah**, Tuesday, December 8, 2009 at 10:00pm
No, I haven't. Thank you so much.

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