Sửa đề: \(P=\dfrac{2}{2x+3}+\dfrac{3}{2x+1}-\dfrac{6x+5}{\left(2x+1\right)\left(2x+3\right)}\)
\(=\dfrac{4x+2+6x+9-6x-5}{\left(2x+1\right)\left(2x+3\right)}\)
\(=\dfrac{4x+6}{\left(2x+1\right)\left(2x+3\right)}=\dfrac{2}{2x+1}\)
Rút gọn \(\left[\dfrac{x}{2x-6}-\dfrac{x^2}{x^2-9}+\dfrac{x}{2x-9}.\left(\dfrac{3}{x}-\dfrac{1}{x-3}\right)\right]:\dfrac{x^2-5x-6}{18-2x^2}\)
Rút gọn \(E=\left[\left(\dfrac{3}{x+1}-\dfrac{x}{x^2+2x+1}\right):\dfrac{2x^2+3x}{x^2+7x}+\dfrac{3}{x+1}\right].\dfrac{x^2+x}{3x+1}\)
Rút gọn \(\left[\dfrac{\left(x-1\right)^2}{3x+\left(x-1\right)^2}-\dfrac{1-2x^2+4x}{x^3-1}+\dfrac{1}{x-1}\right]:\dfrac{x^2+x}{x^3+x}\)
Rút gọn \(\left(\dfrac{1+x}{x}+\dfrac{1}{4x^2}\right)\left(\dfrac{1-2x}{1+2x}-\dfrac{1}{1-4x^2}.\dfrac{1-4x+4x^2}{1+2x}\right)-\dfrac{1}{2x}\)
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) \(\left(3xy+\dfrac{1}{2}x\right)\left(3x^{2y}-3xy^2-1\right)\)
Rút gọn \(A=\left(\dfrac{6x+4}{3\sqrt{3x^3}-8}-\dfrac{\sqrt{3x}}{3x+2\sqrt{3x}+4}\right).\left(\dfrac{1+3\sqrt{3x^3}}{1+\sqrt{3x}}-\sqrt{3x}\right)\)
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 \(x=15\)
\(B=\left[\dfrac{3}{x+1}+\left(\dfrac{3}{x+1}-\dfrac{x}{x^2+2x+1}\right):\dfrac{2x^2+3x}{x+1}\right]:\dfrac{1+3x}{x^2+x}\)
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
