Question

tìm x ạ

\(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{\left(2x-2\right)2x}=\frac{1}{8}\)

có 1 bài này hoy ạ mọi người giúp em giải đi

Ai nhanh và đúng nhất em tích cho 

Nha nha mơn nhìu

Answer 1

\(\Rightarrow2.\left(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{\left(2x-2\right).2x}\right)=\frac{1}{8}.2\).2

\(\Rightarrow\frac{2}{2.4}+\frac{2}{4.6}+...\frac{2}{\left(2x-2\right).2x}=\frac{1}{4}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2x-2}-\frac{1}{2x}=\frac{1}{4}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{2x}=\frac{1}{4}\)

\(\Rightarrow\frac{1}{2x}=\frac{1}{4}\Rightarrow\frac{1}{2x}=\frac{1}{2.2}\)

\(\Rightarrow x=2\)

Answer 2

Đề có sai ko bn ?

Answer 3

=>1/2 - 1/4 + 1/4 -1/6 +1/6- 1/8 +1/2x-2 - 1/2x =1/8

=>1/2 - 1/8 + 1/2x-2 - 1/2x= 1/8

=>3/8 + 1/2x-2 - 1/2x =1/8

=>1/2x-2 - 1/2x = 1/2

=>1/(2x-2) . 2x =1/2

=> (2x-2) . 2x =2

=> 4x² -4x=2

=> (x+1). 4x =2=-2.-1=2.1

=>x+1=-2 =>x=-3

Hay x+1=2 =>x=1

=>4x=1 => x=1/4

Hay 4x=-1 =>x=-1/4

K MK NHA. CHÚC BẠN HỌC GIỎI

Answer 4

dòng đầu tiên mk chỉ nhân 2 thôi nha

sorry

Answer 5

\(\frac{1}{4\left(1.2\right)}+\frac{1}{4\left(2.3\right)}+\frac{1}{4\left(2.3\right)}+...+\frac{1}{4.\left(x-1\right)x}=\frac{1}{8}\)

\(\Rightarrow\frac{1}{4}\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{\left(x-1\right)x}\right)=\frac{1}{8}\)

\(\Rightarrow\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{x-\left(x-1\right)}{\left(x-1\right)x}=\frac{1}{2}\)

\(\Rightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x-1}-\frac{1}{x}=\frac{1}{2}\)

\(\Rightarrow1-\frac{1}{x}=\frac{1}{2}\)

\(\Rightarrow\frac{1}{x}=\frac{1}{2}\)

\(\Rightarrow x=2\)