1.Сократите дробь X-7 / корень из X-7 2.При каких значения переменной дроби X-7 / X+3,...

$1) \frac{x-7}{ \sqrt{x-7} } =\frac{ \sqrt{x-7} ^2}{ \sqrt{x-7} }= \sqrt{x-7} \\ \\ \\ \\ 2)\frac{x-7}{x+3}= \frac{x-6}{x+24} \\ \\ (x-7)(x+24)=(x-6)(x+3) \\ \\ x^{2} +17x-168= x^{2} -3x-18 \\ \\ 17x+3x=-18+168 \\ \\ 20x=150 \\ \\ x=7.5$

$\left \{ {{x-y=3} \atop {2 x^{2} +y^2=9}} \right. \\ \\ \left \{ {{x=y+3} \atop {2 (y+3)^{2} +y^2=9}} \right. \\ \\ 2 y^{2} +12y+18+ y^{2} =9 \\ \\ 3y^{2} +12y+9=0 \\ \\ y^{2} +4y+3=0 \\ \\ D=4^2-4*3=4 \\ \\ y_1= \frac{-4+2}{2}=-1 \\ \\ y_2= \frac{-4-2}{2}=-3 \\ \\ x_1=-1+3=2 \\ \\ x_2=-3+ 3=0$

5. x≥3
x≤7
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__________3___________7__________

x∈[3; 7]

6.
$a_1=17 d=-8 a_{11}=a_1+d(11-1)=17+(-8)*10=-63$