a, `x-1/2=3/4`

`⇒x=3/4+1/2`

`⇒x=5/4`

b, `x+7/8=3/4`

`⇒x=3/4-7/8`

`⇒x=-1/8`

c,`1/2 . x-1/4=-1/2`

`⇒1/2 . x =-1/2 +1/4`

`⇒1/2 . x=-1/4`

`⇒ x =-1/4:1/2`

`⇒x=-1/2`

d, `1/2- 5/6 : x = 2/3`

`⇒5/6 : x=1/2 -2/3`

`⇒ 5/6 : x =-1/6`

`⇒ x= 5/6 : (-1)/6`

`⇒x=-5`

\(\dfrac{x-7}{y-6}=\dfrac{7}{6}\\ \Leftrightarrow6x-42=7y-42\\ \Leftrightarrow6x=7y\\ \Leftrightarrow\dfrac{x}{7}=\dfrac{y}{6}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\dfrac{x}{7}=\dfrac{y}{6}=\dfrac{x-y}{7-6}=\dfrac{-4}{1}=-4\\ \dfrac{x}{7}=-4\Leftrightarrow x=-28\\ \dfrac{y}{6}=-4\Leftrightarrow y=-24\)

Thời gian để ô tô đi từ A đến B là:
10h35'-7h-20'=3h15'=3,25h

Quãng đường AB là:
3,25 x 44 = 143(km)

Đáp số: 143km

\(a,\dfrac{3x+1}{4}=\dfrac{x+2}{3}\\ \Leftrightarrow9x+3=4x+8\\ \Leftrightarrow5x=5\\ \Leftrightarrow x=1\\ b,ĐKXĐ:x\ne0,x\ne5\\ \dfrac{x-3}{x-5}+\dfrac{1}{x}=\dfrac{x+5}{x\left(x-5\right)}\\ \Leftrightarrow\dfrac{x\left(x-3\right)}{x\left(x-5\right)}+\dfrac{x-5}{x\left(x-5\right)}-\dfrac{x+5}{x\left(x-5\right)}=0\\ \Leftrightarrow\dfrac{x^2-3x+x-5-x-5}{x\left(x-5\right)}=0\\ \Rightarrow x^2-3x-10=0\\ \Leftrightarrow\left(x-5\right)\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=5\left(ktm\right)\\x=-2\left(tm\right)\end{matrix}\right.\)

\(c,ĐKXĐ:x\ne0,x\ne-1\\ \dfrac{x+3}{x+1}+\dfrac{x-3}{x}=2\\ \Leftrightarrow\dfrac{x\left(x+3\right)}{x\left(x+1\right)}+\dfrac{\left(x-3\right)\left(x+1\right)}{x\left(x+1\right)}-\dfrac{2x\left(x+1\right)}{x\left(x+1\right)}=0\\ \Leftrightarrow\dfrac{x^2+3x+x^2-2x-3-2x^2-2x}{x\left(x+1\right)}=0\\ \Rightarrow-x-3=0\\ \Leftrightarrow x=-3\left(tm\right)\)

\(d,ĐKXĐ:x\ne0,x\ne-2\\ \dfrac{7}{x}-\dfrac{5}{x+2}=0\\ \Leftrightarrow\dfrac{7\left(x+2\right)}{x\left(x+2\right)}-\dfrac{5x}{x\left(x+2\right)}=0\\ \Leftrightarrow\dfrac{7x+14-5x}{x\left(x+2\right)}=0\\ \Rightarrow2x+14=0\\ \Leftrightarrow x=-7\left(tm\right)\)

\(e,\dfrac{-11}{23}.\dfrac{6}{7}+\dfrac{8}{7}.\dfrac{-11}{23}-\dfrac{1}{23}=\dfrac{-11}{23}\left(\dfrac{6}{7}+\dfrac{8}{7}\right)-\dfrac{1}{23}=\dfrac{-11}{23}.2-\dfrac{1}{23}=\dfrac{-22}{23}-\dfrac{1}{23}=-1\)

\(f,\left(\dfrac{377}{-231}-\dfrac{123}{89}+\dfrac{34}{791}\right)\left(\dfrac{1}{6}-\dfrac{1}{8}-\dfrac{1}{24}\right)\\ =\left(\dfrac{377}{-231}-\dfrac{123}{89}+\dfrac{34}{791}\right)\left(\dfrac{4}{24}-\dfrac{3}{24}-\dfrac{1}{24}\right)\\ =\left(\dfrac{377}{-231}-\dfrac{123}{89}+\dfrac{34}{791}\right).0\\ =0\)

a, Cạnh hình vuông là:

`16/5 : 4 =4/5(m)`

b,Chiều dài hình chữ nhật là:
`4/5 + 1/7 =33/35(m)

`Diện tích hình chữ nhật là:

` 4/5 xx 33/35 = 132/175`(m²)

Ta có: 2012=2011+1=x+1

\(A=x^5-2012x^4+2012x^3-2012x^2+2012x-2012\\ =x^5-\left(x+1\right)x^4+\left(x+1\right)x^3-\left(x+1\right)x^2+\left(x+1\right)x-\left(x+1\right)\\ =x^5-x^5-x^4+x^4+x^3-x^3-x^2+x^2+x-x-1\\ =-1\)

\(a,\dfrac{2}{1.3}+\dfrac{2}{3.5}+...+\dfrac{2}{99.101}=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{99}-\dfrac{1}{101}=1-\dfrac{1}{101}=\dfrac{100}{101}\\ b,\dfrac{5}{1.3}+\dfrac{5}{3.5}+...+\dfrac{5}{99.101}=\dfrac{5}{2}\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+...+\dfrac{2}{99.101}\right) =\dfrac{5}{2}.\dfrac{100}{101}=\dfrac{250}{101}\)

\(c,\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}=\dfrac{1}{2}-\dfrac{1}{100}=\dfrac{49}{100}\\ d,\dfrac{5}{1.4}+\dfrac{5}{4.7}+...+\dfrac{5}{100.103}=\dfrac{5}{3}\left(\dfrac{3}{1.4}+\dfrac{3}{4.7}+...+\dfrac{3}{100.103}\right)=\dfrac{5}{2}.\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{100}-\dfrac{1}{103}\right)=\dfrac{5}{2}.\left(1-\dfrac{1}{103}\right)=\dfrac{5}{2}.\dfrac{102}{103}=\dfrac{255}{103}\)

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