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## anonymous 5 years ago z^2+8z+16/z^2-100 times z^2-10z/z+4=

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1. anonymous

i think the answer is 1

2. anonymous

(z^2+8z+16/z^2-100)*(z^2-10z/z+4) = z^2*(z^2-10z/z+4)+8z*(z^2-10z/z+4)+16/z^2-100*(z^2-10z/z+4) u can finish it right?

3. anonymous

lawd it looks even harder lol

4. anonymous

z^2*(z^2-10z/z+4) = z^4-10z^3/z+4 8z*(z^2-10z/z+4) = 8z^3-80z^2/z+4 16/z^2-100*(z^2-10z/z+4) = (16z^2/z^2-100)-(160z/(z^2-100)(z+4)) from this is easier

5. anonymous

it doesn't nave to be solved simplified

6. anonymous

and then what it has to be?

7. anonymous

simplified

8. anonymous

(z^2+8z+16/z^2-100)*(z^2-10z/z+4) = z^2*(z^2-10z/z+4)+8z*(z^2-10z/z+4)+16/z^2-100*(z^2-10z/z+4) =z^4-10z^3/z+4+8z^3-80z^2/z+4+(16z^2/z^2-100)-(160z/(z^2-100)(z+4)) and you simplify by urself from this

9. anonymous

The problem statement seems to be: $\frac{\left(z^2+8 z+16\right) \left(z^2-10 z\right)}{\left(z^2-100\right) (z+4)}$ Both of the products in the Numertor can be factored as well as the first product of the Denominator. Factor and then simplify. $\frac{(4+z)^2 (-10+z) z}{(-10+z) (10+z) (z+4)}=\frac{z (4+z)}{10+z}$

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