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\(\dfrac{1}{x+1}-\dfrac{1}{x}\) MTC: \(x\left(x+1\right)\)
\(=\dfrac{x}{x\left(x+1\right)}-\dfrac{x+1}{x\left(x+1\right)}\)
\(=\dfrac{x-\left(x+1\right)}{x\left(x+1\right)}\)
\(=\dfrac{x-x-1}{x\left(x+1\right)}\)
\(=\dfrac{-1}{x\left(x+1\right)}\)
Đố :
Đố em tính nhanh được tổng sau :
\(\dfrac{1}{x\left(x+1\right)}+\dfrac{1}{\left(x+1\right)\left(x+2\right)}+\dfrac{1}{\left(x+2\right)\left(x+3\right)}+\dfrac{1}{\left(x+3\right)\left(x+4\right)}+\dfrac{1}{\left(x+4\right)\left(x+5\right)}+\dfrac{1}{\left(x+5\right)\left(x+6\right)}\)
Thực hiện phép trừ :
\(\dfrac{2x}{x-1}-\dfrac{x}{x-1}-\dfrac{1}{x-1}\)
Cách thực hiện nào sau đây sai ?
(A) \(\dfrac{2x}{x-1}-\dfrac{x}{x-1}-\dfrac{1}{x-1}=\left(\dfrac{2x}{x-1}-\dfrac{x}{x-1}\right)-\dfrac{1}{x-1}=......................\)
(B) \(\dfrac{2x}{x-1}-\dfrac{x}{x-1}-\dfrac{1}{x-1}=\dfrac{2x}{x-1}-\left(\dfrac{x}{x-1}-\dfrac{1}{x-1}=..............\right)\)
(C) \(\dfrac{2x}{x-1}-\dfrac{x}{x-1}-\dfrac{1}{x-1}=\dfrac{2x}{x-1}-\left(\dfrac{x}{x-1}+\dfrac{1}{x-1}\right)=........\)
(D) \(\dfrac{2x}{x-1}-\dfrac{x}{x-1}-\dfrac{1}{x-1}=\dfrac{2x}{x-1}+\dfrac{-x}{x-1}+\dfrac{-1}{x-1}=.........\)
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
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)\(\dfrac{x}{x-2}-\dfrac{x}{x+2}+\dfrac{8}{x^2-4}\)
Xét xem các biến đổi sau đúng hay sai và giải thích
a/\(-\dfrac{2x}{x-1}=\dfrac{2x}{x+1}\) b/ \(\dfrac{1-x}{1+x}=\dfrac{x-1}{x+1}\)
c/\(\dfrac{x-4}{x-1}=\dfrac{4-x}{1-x}\) d/\(\dfrac{x-4}{x-1}-\dfrac{3x}{1-z}=\dfrac{x-4}{x-1}+\dfrac{3x}{x-1}=\dfrac{4x-4}{x-1}=4\)
Thực hiện phép tính :
a, \(\dfrac{x^3}{x+1}+\dfrac{x^2}{x-1}+\dfrac{1}{x+1}+\dfrac{1}{1-x}\)
b, \(\dfrac{x^3}{x-1}-\dfrac{x^2}{x+1}-\dfrac{1}{x-1}+\dfrac{1}{x+1}\)
c, \(\dfrac{4-2x+x^2}{2+x}-2-x\)
1) tính
a) \(\dfrac{2}{x^2+2x}+\dfrac{2}{x^2+6x+8}+\dfrac{2}{x^2+10x+24}+\dfrac{2}{x^2+14x+48}\)
b) \(\dfrac{1}{1-x}+\dfrac{1}{1+x}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
\(\dfrac{1}{x-1}-\dfrac{1}{x+1}-\dfrac{2}{x^2+1}-\dfrac{4}{x^4+1}-\dfrac{8}{x^8+1}-\dfrac{16}{x^{16}+1}\)
Tìm x
1 xét xem các biến đổi sau đúng hay sai và giải thích
a) \(-\dfrac{3}{x-4}=\dfrac{2x}{x+1}\)
b) \(\dfrac{1-x}{1+x}=\dfrac{x-1}{x+1}\)
c)\(\dfrac{x-4}{x-1}=\dfrac{4-x}{1-x}\)
d) \(\dfrac{x-4}{x-1}-\dfrac{3x}{1-x}=\dfrac{x-4}{x-1}+\dfrac{3x}{x-1}=\dfrac{4x-4}{x-1}=4\)