\(Q=\dfrac{x^2-3x+3}{\left(x-1\right)^2}\)
\(Q=\dfrac{x^2-2.\dfrac{3}{2}x+\dfrac{9}{4}+\dfrac{3}{4}}{\left(x-1\right)^2}\)
\(Q=\dfrac{\left(x-\dfrac{3}{2}\right)^2+\dfrac{3}{4}}{\left(x-1\right)^2}\)
Để Q có GTNN
=> \(\left(x-\dfrac{3}{2}\right)^2+\dfrac{3}{4}\)phải lớn nhất và (x-1)^2 phải bé nhất
Tìm
Min Q=\(\dfrac{x^2-3x+3}{\left(x-1\right)^2}\forall x\ne1\)
Thực hiện phép tính các đa thức sau
a) \(\left(3x^2-2x+5\right)\left(2x^2-3x+1\right)\)
b) \(\left(\dfrac{3}{2}x^2-\dfrac{2}{3}x-\dfrac{5}{3}\right)\left(4x^2-\dfrac{3}{2}x-3\right)\)
c) \(\left(\dfrac{3}{4}x^2+2x-\dfrac{1}{3}\right)\left(4x^2-\dfrac{3}{2}x-3\right)\)
d) \(\left(-\dfrac{1}{3}+2x-x^2\right)\left(-2x^2-\dfrac{1}{2}x+2\right)\)
e) \(\left(3xy+\dfrac{1}{2}x\right)\left(3x^{2y}-3xy^2-1\right)\)
\(B=\left[\dfrac{3}{x+1}+\left(\dfrac{3}{x+1}-\dfrac{x}{x^2+2x+1}\right):\dfrac{2x^2+3x}{x+1}\right]:\dfrac{1+3x}{x^2+x}\)
Rút gọn \(E=\left[\left(\dfrac{3}{x+1}-\dfrac{x}{x^2+2x+1}\right):\dfrac{2x^2+3x}{x^2+7x}+\dfrac{3}{x+1}\right].\dfrac{x^2+x}{3x+1}\)
\(C=\left(\dfrac{1}{3}+\dfrac{3}{x^2-3x}\right):\left(\dfrac{x^2}{27-3x^2}+\dfrac{1}{x+3}\right)\)
Rút gọn:
\(C=\left[\left(1+\dfrac{1}{x}\right)\cdot\dfrac{2}{x^3+3x^2+3x+1}+\left(1+\dfrac{1}{x^2}\right)\cdot\dfrac{1}{1+2x+x^2}\right]:\dfrac{x-1}{x^3}\)
Rút gọn \(\left[\dfrac{\left(x-1\right)^2}{3x+\left(x-1\right)^2}-\dfrac{1-2x^2+4x}{x^3-1}+\dfrac{1}{x-1}\right]:\dfrac{x^2+x}{x^3+x}\)
Cho biểu thức:
A\(=\left(\dfrac{\left(x+1\right)^2}{\left(x+1\right)^2-3x}-\dfrac{2x^2+4x-1}{x^3+1}-\dfrac{1}{x+1}\right):\dfrac{x^2-4}{3x^2+6x}\)
a/ Rút gọn A
b/ Tìm x ∈ Z để A nguyên
1, Tính
a) \(\dfrac{3x^2-5}{x^2-5x}+\dfrac{5-15x}{5x-25}\)
b) \(\dfrac{4+x^3}{x-3}-\dfrac{2x+2x^2}{x-3}+\dfrac{2x-13}{x-3}\)
c) \(\dfrac{2}{x-5}+\dfrac{x-25}{\left(x+5\right)\left(x-5\right)}\)
d) \(\dfrac{2x+8}{x^2-12+1}+\dfrac{7}{x-2}\)
2. Tính giá trị biểu thức
A= \(2\left(x+1\right)+\left(3x+2\right)\left(3x-2\right)-9x^2\)
tại \(x=15\)