Question

срочно!!!!
алгебра!
даю 44 баллов!​

Answer 1

$1)\frac{a+1}{a-1}-\frac{a}{a+1}=\frac{(a+1)(a+1)-a(a-1)}{(a-1)(a+1)}=\frac{a^{2}+2a+1-a^{2}+a }{(a-1)(a+1)}=\frac{3a+1}{(a-1)(a+1)}\\\\2)\frac{3a+1}{(a-1)(a+1)}:\frac{3a+1}{a^{2}+a }=\frac{3a+1}{(a-1)(a+1)}*\frac{a(a+1)}{3a+1}=\frac{a}{a-1}\\\\Otvet:\boxed{\frac{a}{a-1}}$

$8)\frac{9x^{2}-1 }{3x^{2}-4x+1 }\\\\3x^{2} -4x+1=0\\\\D=(-4)^{2}-4*3*1=16-12=4=2^{2}\\\\x_{1}=\frac{4-2}{6}=\frac{1}{3} \\\\x_{2}=\frac{4+2}{6}=1\\\\3x^{2}-4x+1=3(x-\frac{1}{3})(x-1)=(3x-1)(x-1)\\\\\frac{9x^{2}-1 }{3x^{2}-4x+1 }=\frac{(3x-1)(3x+1)}{(3x-1)(x-1)}=\frac{3x+1}{x-1}\\\\Otvet:\boxed{\frac{3x+1}{x-1}}$