tex] пж до завтра...

July 2022 1 27 Report

1. [tex]\frac{a-1}{a+1} -\frac{a+1}{a-1} +\frac{4}{a^{2}-1\\ }[/tex]
2.[tex]\frac{b-2}{b+2} -\frac{b+2}{b-2} -\frac{16}{b^{2}-4 }[/tex]
пж до завтра

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$1)\frac{a-1}{a+1}-\frac{a+1}{a-1}+\frac{4}{a^{2}-1 }=\frac{a-1 }{a+1}-\frac{a+1}{a-1}+\frac{4}{(a-1)(a+1)}=\frac{(a-1)^{2}-(a+1)^{2}+4}{(a-1)(a+1)}=\frac{a^{2}-2a+1-a^{2}-2a-1+4}{(a-1)(a+1)}=\frac{-4a+4}{(a-1)(a+1)}=-\frac{4(a-1)}{(a-1)(a+1)}=-\frac{4}{a+1}\\\\Otvet:\boxed{-\frac{4}{a+1}}$

$2)\frac{b-2}{b+2}-\frac{b+2}{b-2}-\frac{16}{b^{2}-4}=\frac{b-2}{b+2}-\frac{b+2}{b-2}-\frac{16}{(b-2)(b+2)}=\frac{(b-2)^{2}-(b+2)^{2}-16}{(b-2)(b+2)}=\frac{b^{2}-4b+4-b^{2}-4b-4-16}{(b-2)(b+2)}=\frac{-8b-16}{(b-2)(b+2)}=-\frac{8(b+2)}{(b-2)(b+2)}=-\frac{8}{b-2}=\frac{8}{2-b}\\\\Otvet:\boxed{\frac{8}{2-b}}$

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