Question

Упростите:
$frac{z+5}{2z^{2}-2} + frac{3}{1-z}+frac{5}{1-z^{2}}$

Answer 1

решение во вложении

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d2fb6f252c0b388e99ff036c7c5d5b6a.doc

73ad6e0a4c41a1faab398cade1619dc0.doc

Answer 2

$frac{z+5}{2z^{2}-2} + frac{3}{1-z}+frac{5}{2z+2}}=-frac{3}{(z-1)(z+1)}$

1) $frac{z+5}{2z^{2}-2}+frac{3}{1-z}=frac{z+5}{2(z^{2}-1)}+frac{3}{-z+1}=frac{z+5}{2(z-1)(z+1)}+frac{3}{-(z-1)}=frac{z+5-3cdot2(z+1)}{2(z-1)(z+1)}=frac{z+5-6(z+1)}{2(z-1)(z+1)}=$=$frac{z+5-6z-6}{2(z-1)(z+1)}=frac{(z-6z)+(5-6)}{2(z-1)(z+1)}=frac{-5z-1}{2(z-1)(z+1)}= frac{-(5z+1)}{2(z-1)(z+1)}=-frac{5z+1}{2(z-1)(z+1)}$

2) $-frac{5z+1}{2(z-1)(z+1)}+frac{5}{2z+2}}=frac{5}{2(z+1)}-frac{5z+1}{2(z-1)(z+1)}=frac{5(z-1)-(5z+1)}{2(z-1)(z+1)}=frac{5z-5-5z-1}{2(z-1)(z+1)}=frac{(5z-5z)+(-1-5)}{2(z-1)(z+1)}=$=$frac{-6}{2(z-1)(z+1)}=frac{-3}{(z-1)(z+1)}=-frac{3}{(z-1)(z+1)}$

d2fb6f252c0b388e99ff036c7c5d5b6a.doc

73ad6e0a4c41a1faab398cade1619dc0.doc