Упростите выражение [tex](\frac{a-5}{a^{2}-5a+25} - \frac{12a-61}{a^{3}+125}) : \frac{3a-18}{2a^{2}-10a+50}[/tex]. Created by littlesleep. algebra-ru

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Упростите выражение

[tex](\frac{a-5}{a^{2}-5a+25} - \frac{12a-61}{a^{3}+125}) : \frac{3a-18}{2a^{2}-10a+50}[/tex]

triolana

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irkarom

$(\frac{a-5}{a^{2}-5a+25} - \frac{12a-61}{a^{3}+125}) : \frac{3a-18}{2a^{2}-10a+50} =\\ \\ (\frac{a-5}{a^{2}-5a+25} - \frac{12a-61}{(a+5)(a^{2}-5a+25)}) : \frac{3(a-6)}{2(a^{2}-5a+25)}=\\ \\ 1) \frac{a-5}{a^{2}-5a+25} - \frac{12a-61}{(a+5)(a^{2}-5a+25)} = \frac{(a-5)(a+5)-12a + 61}{(a+5)(a^{2}-5a+25)} = \frac{a^{2} - 25-12a + 61}{(a+5)(a^{2}-5a+25)} = \\ \\ \frac{a^{2} -12a + 36}{(a+5)(a^{2}-5a+25)} =\frac{(a-6)^{2}}{(a+5)(a^{2}-5a+25)} \\ \\$

$2) \frac{(a-6)^{2}}{(a+5)(a^{2}-5a+25)} : \frac{3(a-6)}{2(a^{2}-5a+25)}=\\ \\ =\frac{(a-6)^{2}}{(a+5)(a^{2}-5a+25)} * \frac{2(a^{2}-5a+25)}{3(a-6))}= \\ \\ =\frac{2(a-6)}{3(a+5)}$

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