Question

Выражение: 1) a-15\4a-20 - a-5/4a+20 + 30\a²-25; 2) 8a³+100a\a³+125 - 4a²\a²-5a+25. ! нужно !

Answer 1

$\tt\displaystyle 1)\ \bold{\frac{5}{a^2-25} }$

$\tt\displaystyle 2)\ \bold{\frac{4a}{a+5} }$

Объяснение:

$\tt\displaystyle \frac{a-15}{4a-20}-\frac{a-5}{4a+20}+\frac{30}{a^2-25}=\frac{a-15}{4(a-5)}-\frac{a-5}{4(a+5)}+\frac{30}{(a-5)(a+5)} =\\\\\\=\frac{(a+5)(a-15)-(a-5)(a-5)+30*4}{4(a-5)(a+5)} =\\\\\\=\frac{a^2-10a-75-a^2+10a-25+120}{4(a-5)(a+5)}=\frac{20}{4(a^2-25)}=\frac{5}{a^2-25}$

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$\tt\displaystyle \frac{8a^3+100a}{a^3+125}-\frac{4a^2}{a^2-5a+25}=\frac{8a^3+100a}{(a+5)(a^2-5a+25)}-\frac{4a^2}{a^2-5a+25}=\\\\\\=\frac{8a^3+100a-4a^2(a+5)}{(a+5)(a^2-5a+25)}=\frac{8a^3+100a-4a^3-20a^2}{(a+5)(a^2-5a+25)}=\\\\\\=\frac{4a^3-20a^2+100a}{(a+5)(a^2-5a+25)} =\frac{4a(a^2-5a+25)}{(a+5)(a^2-5a+25)} =\frac{4a}{a+5}$