Question

Докажите тождество:
$( \frac{a + 5}{5a - 1} + \frac{a + 5}{a + 1}) \div \frac{ {a}^{2} + 5a }{1 - 5a} + \frac{ {a}^{2} + 5 }{a + 1} = a - 1$
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Answer 1

Объяснение:

$1)\ \\\frac{a+5}{5a-1}+\frac{a+5}{a+1} =(a+5)*( \frac{1}{5a-1}+\frac{1}{a+1})=(a+5)*(\frac{a+1+5a-1}{(5a-1)*(a+1)})=\frac{6a*(a+5)}{(5a-1)*(a+1)} .\\2)\ \\\frac{6a*(a+5)}{(5a-1)*(a+1)}:\frac{a^2+5a}{1-5a}=\frac{6a*(a+5)}{(5a-1)*(a+1)}*(-\frac{5a-1}{a*(a+5)} )=-\frac{6}{a+1}.\\3)\\ -\frac{6}{a+1}+\frac{ a^2+5}{a+1}=\frac{a^2+5-6}{a+1}=\frac{a^2-1}{a+1}=\frac{(a+1)*(a-1)}{a+1} =a-1.$