Question

Упростить выражение ( с подробным решением )
$(\frac{6a+1}{a^{2}-6a } + \frac{6a-1}{a^{2}+6a } ) * \frac{a^{2}-36 }{a^{2}+1 }$

Answer 1

$(\frac{6a+1}{a^2-6a}+\frac{6a-1}{a^2+6a})\cdot\frac{a^2-36}{a^2+1}=\\ \\=(\frac{6a+1}{a(a-6)}+\frac{6a-1}{a(a+6)})\cdot\frac{(a-6)(a+6)}{a^2+1} =\\ \\=\frac{(6a+1)(a+6)+(6a-1)(a-6)}{a(a-6)(a+6)}\cdot\frac{(a-6)(a+6)}{a^2+1} =\\ \\=\frac{6a^2+a+36a+6+6a^2-a-36a+6}{a(a^2+1)}= \frac{12a^2+12}{a(a^2+1)}=\frac{12(a^2+1)}{a(a^2+1)}=\frac{12}{a}$

Answer 2

$( \frac{6a + 1}{a {}^{2} - 6a } + \frac{6a - 1}{a {}^{2} + 6a} ) \times \frac{a {}^{2} - 36 }{a {}^{2} + 1} =12a {}^{ - 1} \\ \\ 1)\: \frac{(6a + 1)(a {}^{2} + 6a) + (6a - 1)(a {}^{2} - 6a) }{(a {}^{2} - 6a)(a {}^{2} + 6a)} = \frac{12a(a {}^{2} + 1) }{(a {}^{2} - 6a)(a {}^{2}+ 6a)} \\ \\ 2) \: \frac{12a(a {}^{2} + 1) }{a {}^{2}(a - 6)(a + 6) } \times \frac{(a - 6)(a + 6)}{a {}^{2} + 1 } = \frac{12a}{a {}^{2} } = \frac{12}{a} = 12a {}^{ - 1}$