Question

Спростити вираз якщо a=2/3

Answer 1

$\frac{a}{a^2-1}+\frac{a^2+a-1}{a^3-a^2+a-1}+\frac{a^2-a-1}{a^3+a^2+a+1}-\frac{2a^3}{a^4-1} =\frac{a}{a^2-1}-\frac{2a^3}{a^4-1}+\frac{a^2+a-1}{a^2(a-1)+a-1}+\frac{a^2-a-1}{a^2(a+1)+a+1}=\frac{a(a^2+1)-2a^3}{a^4-1}+\frac{a^2+a-1}{(a-1)(a^2+1)}+\frac{a^2-a-1}{(a+1)(a^2+1)} =\frac{a^3+a-2a^3}{a^4-1}+\frac{(a^2+a-1)(a+1)}{(a^2-1)(a^2+1)}+\frac{(a^2-a-1)(a-1)}{(a^2-1)(a^2+1)} =\frac{a-a^3+a^3+a^2-a+a^2+a-1+a^3-a^2-a-a^2+a+1}{a^4-1}=\frac{a^3+1}{a^4-1} =[tex] \frac{\frac{27}{8}+1}{\frac{81}{16}-1} =\frac{54+16}{81-16} = \frac{70}{65} =\frac{14}{13} =1\frac{1}{13}$ = [/tex]