Question

Упростите выражение 

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

Answer 1

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e219364d239764f746dbc6b95092fed7.pdf

Answer 2

 

 

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

 

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

e219364d239764f746dbc6b95092fed7.pdf