\(=\dfrac{x+1-1}{x+1}\cdot\dfrac{x+2-1}{x+2}\cdot...\cdot\dfrac{x+2018-1}{x+2018}\)
\(=\dfrac{x}{x+1}\cdot\dfrac{x+1}{x+2}\cdot...\cdot\dfrac{x+2017}{x+2018}\)
\(=\dfrac{x}{x+2018}\)
Thực hiện phép tính:
\(a,\dfrac{1}{x\left(x+1\right)}+\dfrac{1}{\left(x+1\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+3\right)}+\dfrac{1}{\left(x+3\right)\left(x+4\right)}\)
\(b,\dfrac{1}{x^2+3x+2}+\dfrac{1}{x^2+5x+6}+\dfrac{1}{x^2+7x+12}+\dfrac{1}{x^2+9x+20}\)
Cho hỏi caćh làm ạ!!
Rút gọn:
\(\dfrac{1}{x\left(x+1\right)}+\dfrac{1}{\left(x+1\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+3\right)}+.......\dfrac{1}{\left(x+2017\right)\left(x+2018\right)}\)
1.rút gọn biểu thuc P=\(\dfrac{2}{x+3}+\dfrac{1}{x-3}+\dfrac{9-x}{9-x^2}\) với x\(\ne-3vàx\ne3\)
2.thực hiện phép tính \(\left(2x^4-3x^3-3x^2+6x-1\right):\left(x^2-2\right)\)
\(\left(15x^4y^6-12^3y^4-18x^2y^3\right):\left(-6x^2y^2\right)\)
Thực hiện phép tính:
\(a,\left(x-\dfrac{x^2+y^2}{x+y}\right)\left(\dfrac{1}{y}+\dfrac{2}{x-y}\right)\)
\(b,\left(\dfrac{2}{x^2-1}+\dfrac{x^2-3}{3x^2-1}\right):\left[\dfrac{1}{x}-\dfrac{2x\left(x^2-3\right)}{\left(x^2-1\right)\left(3x^2-1\right)}\right]\)
giải pt: \(\dfrac{1}{\left(x-1\right)\left(x-2\right)}+\dfrac{1}{\left(x-3\right)\left(x-2\right)}=\dfrac{1}{\left(x-3\right)\left(x-4\right)}+\dfrac{1}{\left(x-1\right)\left(x-4\right)}\)
thực hiên phép tính
a.\(\dfrac{x^2+y^2}{4\left(x+y\right)}+\dfrac{2xy}{4\left(x+y\right)}\)
b.\(\dfrac{x+5}{2x-2}-\dfrac{4}{x^2-1}:\dfrac{2}{x+1}\)
Thực hiện phép tính:
\(\dfrac{1}{x\left(x+y\right)}+\dfrac{1}{y\left(x+y\right)}+\dfrac{1}{x\left(x-y\right)}+\dfrac{1}{y\left(y-x\right)}\)
Thực hiện phép tính:
a) \(\dfrac{x+1}{x+2}:\left(\dfrac{x+2}{x+3}:\dfrac{x+3}{x+1}\right)\)
b, \(\dfrac{8}{\left(x^2+3\right)\left(x^2-1\right)}+\dfrac{2}{x^2+3}+\dfrac{1}{x+1}\)
c, \(\dfrac{x+y}{2\left(x-y\right)}-\dfrac{x-y}{2\left(x+y\right)}+\dfrac{2y^2}{x^2-y^2}\)
d,\(\dfrac{x-1}{x^3}-\dfrac{x+1}{x^3-x^2}+\dfrac{3}{x^3-2x^2+x}\)
Tính
\(A=\dfrac{1}{x\left(x+1\right)}+\dfrac{1}{\left(x+1\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+3\right)}+.....+\dfrac{1}{\left(x+2013\right)\left(x+2014\right)}\)
