Câu 03: (a) Rût gơn biểu thực \[ \left(\frac{1-x}{x^{2}+x^{3}-x^{4}}-\frac{x^{2}+x+2}{x^{5}-x^{3}-2 x^{2}-x}\right):\left(\frac{1+x^{4}}{x^{3}+x^{4}+x^{5}}-\frac{1-x+x^{2}}{x}\right) \] (b) Phân tích phân thức \( \frac{1}{(x-1)(x-2)(x-3)(x-4)} \) thành tổng các phân thức dơn giản.

\( \sqrt { n ^ { 2 } - 1 } - ( n + 1 ) = \frac { ( n ^ { 2 } - 1 ) - ( n + 1 ) ^ { 2 } } { \sqrt { n ^ { 2 } - 1 } + ( n + 1 ) } = \frac { - 2 n - 2 } { \sqrt { n ^ { 2 } - 1 } + ( n + 1 ) } \rightarrow - 1 \)

268. Решите уравнение: \( \begin{array}{l}\text { а) }(y+2)\left(y^{2}-2 y+4\right)-y(y-3)(y+3)=44 \text {; } \\ \text { б) }(m-3)\left(m^{2}+3 m+9\right)-m(m+2)(m-2)=13 \text {; } \\ \text { B) }(3 a+1)\left(9 a^{2}-3 a+1\right)-3 a\left(9 a^{2}+4\right)=25 \text {; }(2 n-1)\left(4 n^{2}+2 n+1\right)-4 n\left(2 n^{2}-5\right)=21 \text {. }\end{array} \).

268. Решите уравнение: \( \begin{array}{l}\text { а) }(y+2)\left(y^{2}-2 y+4\right)-y(y-3)(y+3)=44 \text {; } \\ \text { б) }(m-3)\left(m^{2}+3 m+9\right)-m(m+2)(m-2)=13 \text {; } \\ \text { (B) }(3 a+1)\left(9 a^{2}-3 a+1\right)-3 a\left(9 a^{2}+4\right)=25 \text {; } \\ \text { (A) }(2 n-1)\left(4 n^{2}+2 n+1\right)-4 n\left(2 n^{2}-5\right)=21 \text {. }\end{array} \)

Вычислить следующие определители: а) \( \left|\begin{array}{cc}1 & -2 \\ -2 & 4\end{array}\right| \); б) \( \left|\begin{array}{ccc}1 & 2 & 0 \\ 0 & 0 & 3 \\ 5 & 0 & -1\end{array}\right| \), 2. Найти точку пересечения прямых \( l_{1}: 3 x-2 y=0 \) и \( l_{2}: y=-x+5 \). Построить прямые.

Evaluate the following function. Your answer should be an integer. \( f(x)=-3^{2 x-2} \), for \( x=3 \) Your answer is \( f(3)=\square \)