a) 3 3/4 . x = 1 1/2

<=> 15/4 . x = 3/2

<=> x = 3/4 . 4/15

<=> x = 1/5

Vậy x = 1/5

b) 1 1/4 x + 1 1/2 = 1 1/4

<=> 5/4 . x + 3/2 = 5/4

<=> 5/4 . x = 5/4 - 3/2

<=> 5/4 . x = -1/4

<=> x = -1/4 . 4/5

<=> x = -1/5

Vậy x = -1/5

c) ( 3 1/3 - 1 1/2 x ) : 5/6 = 1 1/2

<=> ( 10/3 - 3/2 x ) : 5/6 = 3/2

<=> 10/3 - 3/2 x = 3/2 . 5/6

<=> 10/3 - 3/2 x = 5/4

<=> 3/2 . x = 10/3 - 5/4

<=> 3/2 . x = 25/12

<=> x = 25/12 . 2/3

<=> x = 25/18

Vậy x = 25/18

d) ( 3/7 x - 1 ) : 4 = -1/28

<=> 3/7 . x - 1 = -1/28 . 1/4

<=> 3/7 . x - 1 = -1/112

<=> 3/7 . x = -1/112 + 1

<=> 3/7 . x = 111/112

<=> x = 111/112 . 7/3

<=> x = 37/16

Vậy x = 37/16

e) | x - 3/4 | = 1

<=> x - 3/4 = 1

hoặc x - 3/4 = -1

<=> x = 1 + 3/4

hoặc x = -1 + 3/4

<=> x = 7/4

hoặc x = -1/4

Vậy x = 7/4 ; x = -1/4

f) | 2/3 . x + 1/3 | = 5/6

<=> 2/3 . x + 1/3 = 5/6

hoặc 2/3 . x + 1/3 = -5/6

<=> 2/3 . x = 5/6 - 1/3

hoặc 2/3 . x = -5/6 - 1/3

<=> 2/3 . x = 1/2

hoặc 2/3 . x = -7/6

<=> x = 1/2 . 3/2

hoặc x = -7/6 . 3/2

<=> x = 3/4

hoặc x = -7/4

Vậy x = 3/4 ; x = -7/4

\(B=1+5+5^2+5^3+...+5^{2008}+5^{2009}\)

\(\Rightarrow 5B=5+5^2+5^3+5^4+...+5^{2009}+5^{2010}\)

Trừ theo vế:

\(5B-B=(5+5^2+5^3+5^4+...+5^{2009}+5^{2010})-(1+5+5^2+...+5^{2009})\)

\(4B=5^{2010}-1\)

\(B=\frac{5^{2010}-1}{4}\)

\(S=\frac{3^0+1}{2}+\frac{3^1+1}{2}+\frac{3^2+1}{2}+..+\frac{3^{n-1}+1}{2}\)

\(=\frac{3^0+3^1+3^2+...+3^{n-1}}{2}+\frac{\underbrace{1+1+...+1}_{n}}{2}\)

\(=\frac{3^0+3^1+3^2+..+3^{n-1}}{2}+\frac{n}{2}\)

Đặt \(X=3^0+3^1+3^2+..+3^{n-1}\)

\(\Rightarrow 3X=3^1+3^2+3^3+...+3^{n}\)

Trừ theo vế:

\(3X-X=3^n-3^0=3^n-1\)

\(\Rightarrow X=\frac{3^n-1}{2}\). Do đó \(S=\frac{3^n-1}{4}+\frac{n}{2}\)

\(A=1+\frac{3}{2^3}+\frac{4}{2^4}+\frac{5}{2^5}+...+\frac{100}{2^{100}}\)

\(\Rightarrow 2A=2+\frac{3}{2^2}+\frac{4}{2^3}+\frac{5}{2^4}+...+\frac{100}{2^{99}}\)

Trừ theo vế:

\(2A-A=1+\frac{3}{2^2}+\frac{4-3}{2^3}+\frac{5-4}{2^4}+\frac{6-5}{2^5}+...+\frac{100-99}{2^{99}}-\frac{100}{2^{100}}\)

\(\Leftrightarrow A=1+\frac{3}{4}-\frac{100}{2^{100}}+(\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{99}})\)

Đặt \(T=(\frac{1}{2^3}+\frac{1}{2^4}+...+\frac{1}{2^{99}})\)

\(\Rightarrow 2T=\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{98}}\)

Trừ theo vế: \(2T-T=\frac{1}{2^2}-\frac{1}{2^{99}}\)

\(\Leftrightarrow T=\frac{1}{4}-\frac{1}{2^{99}}\)

Do đó: \(A=1+\frac{3}{4}-\frac{100}{2^{100}}+\frac{1}{4}-\frac{1}{2^{99}}=2-\frac{102}{2^{100}}\)

1)

a) \(-\frac{9}{34}:\frac{17}{4}\)

\(=-\frac{18}{289}.\)

b) \(1\frac{1}{2}.\frac{1}{24}\)

\(=\frac{3}{2}.\frac{1}{24}\)

\(=\frac{1}{16}.\)

c) \(-\frac{5}{2}:\frac{3}{4}\)

\(=-\frac{10}{3}.\)

d) \(4\frac{1}{5}:\left(-2\frac{4}{5}\right)\)

\(=\frac{21}{5}:\left(-\frac{14}{5}\right)\)

\(=-\frac{3}{2}.\)

Mấy câu sau bạn đăng ríu rít quá khó nhìn lắm.

Chúc bạn học tốt!

T=(a*2/3):5/6 a:8/15 với a=-4/5

I=3/4*a+4/9*a-1/4*a với a=12/5

P=a(b+1/5)-a*(6/5+b) với a= 2004 ;b=206

Q=1/19*a+3*b:5/7+9/4 với a=38;b=-10/7

V=3/2*(a+b+c)- 1/5*(a-b-c) với a=1/3;b=-5/6;c=3/4

giúp mình với

T=(a*2/3):5/6 a:8/15 với a=-4/5

I=3/4*a+4/9*a-1/4*a với a=12/5

P=a(b+1/5)-a*(6/5+b) với a= 2004 ;b=206

Q=1/19*a+3*b:5/7+9/4 với a=38;b=-10/7

V=3/2*(a+b+c)- 1/5*(a-b-c) với a=1/3;b=-5/6;c=3/4

giúp mình với

bạn ơi !!!

đăng từng câu thôi thế này nhìn loạn cả mắt luôn á

rối mắt quá

a, 2/3+1/3:x=-7

1/3:x=-7-2/3

1/3:x=-23/3

x=1/3:-23/3

x=-1/23

Vậy x=-1/23

c, (2x-3)(6-2x)=0

*TH1: 2x-3=0

2x=3

x=3/2

*TH2: 6-2x=0

2x=6

x=6/2

x=3

Vậy x=3/2 hoặc x=3

d,x:3/4+1/4=-2/3

x:3/4=-2/3-1/4

x:3/4=-11/12

x=-11/12*3/4

x=-11/16

         Bài 1:

- \(\dfrac{11}{2}x\) + 1 = \(\dfrac{1}{3}x-\dfrac{1}{4}\)

- \(\dfrac{11}{2}\)\(x\) - \(\dfrac{1}{3}\)\(x\) = - \(\dfrac{1}{4}\) - 1

-(\(\dfrac{33}{6}\) + \(\dfrac{2}{6}\))\(x\) = - \(\dfrac{5}{4}\)

- \(\dfrac{35}{6}\)\(x\) = - \(\dfrac{5}{4}\)

  \(x=-\dfrac{5}{4}\) : (- \(\dfrac{35}{6}\))

 \(x\) = \(\dfrac{3}{14}\)

Vậy \(x=\dfrac{3}{14}\)

Bài 2: 2\(x\) - \(\dfrac{2}{3}\) - 7\(x\) = \(\dfrac{3}{2}\) - 1

         2\(x\) - 7\(x\) = \(\dfrac{3}{2}\) - 1 + \(\dfrac{2}{3}\)

         - 5\(x\)    = \(\dfrac{9}{6}\) - \(\dfrac{6}{6}\) + \(\dfrac{4}{6}\) 

        - 5\(x\)    = \(\dfrac{7}{6}\)

           \(x\)    = \(\dfrac{7}{6}\) : (- 5) 

          \(x\)    = - \(\dfrac{7}{30}\)

Vậy \(x=-\dfrac{7}{30}\)

Bài 3: \(\dfrac{3}{2}\)\(x\) - \(\dfrac{2}{5}\) = \(\dfrac{1}{3}x\) - \(\dfrac{1}{4}\)

           \(\dfrac{3}{2}\)\(x\) - \(\dfrac{1}{3}x\) = \(-\dfrac{1}{4}\) + \(\dfrac{2}{5}\)

           (\(\dfrac{9}{6}\) - \(\dfrac{2}{6}\))\(x\) = \(\dfrac{-5}{20}\) + \(\dfrac{8}{20}\)

            \(\dfrac{7}{6}x\)       = \(\dfrac{3}{20}\)

            \(x\)       = \(\dfrac{3}{20}\) : \(\dfrac{7}{6}\)

            \(x\)      = \(\dfrac{9}{70}\)

Vậy  \(x=\dfrac{9}{70}\)

\(3,\\ a,=a^2+2a+1-a^2+2a-1-3a^2+3=-3a^2+4a+3\\ b,=\left(m^3-m+1-m^2+3\right)^2=\left(m^3-m^2-m+4\right)^2\\ 4,\\ a,\Leftrightarrow25x^2+10x+1-25x^2+9=3\\ \Leftrightarrow10x=-7\Leftrightarrow x=-\dfrac{7}{10}\\ b,\Leftrightarrow-9x^2+30x-25+9x^2+18x+9=30\\ \Leftrightarrow48x=46\Leftrightarrow x=\dfrac{23}{24}\\ c,\Leftrightarrow x^2+8x+16-x^2+1=16\\ \Leftrightarrow8x=-1\Leftrightarrow x=-\dfrac{1}{8}\)

Ta có:

\(M=\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+\frac{1}{1+2+3+4+5}\)

\(M=\frac{1}{\left(2\times3\right):2}+\frac{1}{\left(3\times4\right):2}+\frac{1}{\left(4\times5\right):2}+\frac{1}{\left(5\times6\right):2}\)

\(M=\frac{2}{2\times3}+\frac{2}{3\times4}+\frac{2}{4\times5}+\frac{2}{5\times6}\)

\(M:2=\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}\)

\(M:2=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)

\(M:2=\frac{1}{2}-\frac{1}{6}\)

\(M:2=\frac{1}{3}\)

\(\Rightarrow M=\frac{1}{3}\times2\)

\(\Rightarrow M=\frac{2}{3}\)