\(\dfrac{1}{x\left(x+1\right)}+\dfrac{1}{\left(x+1\right)\left(x+2\right)}+...+\dfrac{1}{\left(x+6\right)\left(x+7\right)}+\dfrac{1}{\left(x+7\right)\left(x+8\right)}\)
\(=\dfrac{1}{x}-\dfrac{1}{x+1}+\dfrac{1}{x+1}-\dfrac{1}{x+2}+...+\dfrac{1}{x+7}-\dfrac{1}{x+8}\)
\(=\dfrac{1}{x}-\dfrac{1}{x+8}=\dfrac{8}{x\left(x+8\right)}\)
a) x+1/2x-6-4/2x-6 b) 3x-4/6x+3-x-5/6x+3
c) x-1/x-3-3x-8/3-x+3-2x/x-3 d) 3/x+5-5/x-7
e) 3/x+5-5/x-7 f) 2/x-2+3/x+2+5x-18/x2-4
Trừ phân thức:
a) x^2+y^2/(x-y)^3 - 2xy/(x-y)^3.
b) x^2+25y^2/x^2-25y^2 - 10xy/x^2-25y^2.
c)3x/5x+5y - x/10x-10y.
d) 1/x-3 - 3/2x+6 - x/2x^2-12x+18.
e) (x^2-1) - x^4-3x^2-4/x^2+1.
f) 1/3x-2 - 4/3x+2 - 3x-6/4-9x^2.
g) 4x^2-3x+5/x^3-1 - 1-2x/x^2+x+1 - 6/x-1.
h) 5/x+1 - 10/x-x^2-1 - 15/x^3+1.
i) 2/2x+1 - 1/2x-1 - 2/4x^2-1.
Đố :
Đố em tính nhanh được tổng sau :
\(\dfrac{1}{x\left(x+1\right)}+\dfrac{1}{\left(x+1\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+3\right)}+\dfrac{1}{\left(x+3\right)\left(x+4\right)}+\dfrac{1}{\left(x+4\right)\left(x+5\right)}+\dfrac{1}{\left(x+5\right)\left(x+6\right)}\)
a)\(\dfrac{2}{x+2}-\dfrac{1}{x+3}+\dfrac{2x+5}{\left(x+2\right)\left(x+3\right)}\)
b)\(\dfrac{2}{x+1}-\dfrac{1}{x+5}+\dfrac{2x+6}{\left(x+5\right)\left(x+1\right)}\)
c)\(\dfrac{-6}{x^2-9}-\dfrac{1}{x+3}+\dfrac{3}{x-3}\)
d)\(\dfrac{x}{x-2}-\dfrac{x}{x+2}+\dfrac{8}{x^2-4}\)
Thực hiện phép tính: A, x-2 - x^2-10/x+2 B, x/y^2- xy - y/xy-x^2 C, 1/x(x-1) + 1/x-1(x-2) + 1/(x-2)(x-3) + 1/(x-3)(x-4) + 1/(x-4)(x-5) Giúp mình bài này với ạ
bài 1: tính
a, A= 2x-9/x2-5x+6 - x+3/x-2 - 2x+1/3-x
b, B= 2x+1/x2-7x+12 - x+3/x-4 + 2x+1/x-3
c, C= x+2/x+3 - 5/x2+x-6 + 1/2-x
d, D= 3(x2+x-3)/x2+x-2 + x+3/x+2 - x-2/x-1
Bài 1: Thực hiện phép chia:
a) \(\dfrac{5}{x}+\dfrac{x}{x+6}-\dfrac{30}{x^2+6x}\) với x ≠ -6 và x ≠ 0
b) \(\dfrac{3x+1}{\left(x-1\right)^2}-\dfrac{1}{x+1}+\dfrac{x+3}{1-x^2}\) với x ≠ \(\pm\)1
c) \(\dfrac{3x^2+2x+1}{x^3-1}-\dfrac{1-x}{x^2+x+1}-\dfrac{2}{x-1}\) với x ≠ 1
Rút gọn biểu thức :
a) \(\dfrac{3x^2+5x+1}{x^3-1}-\dfrac{1-x}{x^2-6x+9}-\dfrac{3}{x-1}\)
b) \(\dfrac{1}{x^2-x+1}+1-\dfrac{x^2+2}{x^3+1}\)
c) \(\dfrac{7}{x}-\dfrac{x}{x+6}+\dfrac{36}{x^2+6x}\)
a). Chứng minh: \(\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{1}{x\left(x+1\right)}\)
b). Tính nhẩm tổng sau:
\(\dfrac{1}{x\left(x+1\right)}+\dfrac{1}{\left(x+1\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+3\right)}+\dfrac{1}{\left(x+3\right)\left(x+4\right)}+\dfrac{1}{\left(x+4\right)\left(x+5\right)}+\dfrac{1}{x+5}\)
