Question

Спростіть вираз (a²/(a+5)-a³/(a²+10a+25)):(a/(a+5)-a²/(a²-25))

Answer 1

$( \frac{ {a}^{2} }{a + 5} - \frac{ {a}^{3} }{ {a}^{2} +10a+25}):( \frac{a}{a + 5} - \frac{ {a}^{2} }{ {a}^{2} - 25 } ) = ( \frac{ {a}^{2} }{a + 5} - \frac{ {a}^{3} }{ {(a + 5)}^{2} }):( \frac{a}{a + 5} - \frac{ {a}^{2} }{(a + 5)(a - 5) } ) = ( \frac{ {a}^{2}(a + 5) - {a}^{3} }{ {(a + 5)}^{2} }):(\frac{ a(a - 5) - {a}^{2} }{(a + 5)(a - 5) } ) =( \frac{ {a}^{3}+ 5a - {a}^{3} }{ {(a + 5)}^{2} }):(\frac{ {a}^{2} - 5a - {a}^{2} }{(a + 5)(a - 5) } ) =\frac{5a }{ {(a + 5)}^{2} }:\frac{- 5a}{(a + 5)(a - 5) } =\frac{5a }{ {(a + 5)}^{2} } \times \frac{(a + 5)(a - 5)}{ - 5a} = - \frac{a - 5}{a + 5} = \frac{5 - a}{5 + a}$