\(\frac{x+1}{9}+\frac{x+4}{6}+\frac{x+5}{5}=\frac{x+2}{8}+\frac{x+3}{7}+\frac{x+6}{4}\)

\(\Rightarrow\frac{x+1}{9}+\frac{x+4}{6}+\frac{x+5}{5}+3=\frac{x+2}{8}+\frac{x+3}{7}+\frac{x+6}{4}+3\)

\(\Rightarrow\left(\frac{x+1}{9}+1\right)+\left(\frac{x+4}{6}+1\right)+\left(\frac{x+5}{5}+1\right)=\left(\frac{x+2}{8}+1\right)\)\(+\left(\frac{x+3}{7}+1\right)+\left(\frac{x+6}{4}\right)\)

\(\Rightarrow\frac{x+10}{9}+\frac{x+10}{6}+\frac{x+10}{5}=\frac{x+10}{8}+\frac{x+10}{7}+\frac{x+10}{4}\)

\(\Rightarrow\left(x+10\right)\left(\frac{1}{9}+\frac{1}{6}+\frac{1}{5}\right)=\left(x+10\right)\left(\frac{1}{8}+\frac{1}{7}+\frac{1}{4}\right)\)

\(\Rightarrow\left(x+10\right)\frac{43}{90}=\left(x+10\right)\frac{29}{56}\)

\(\Rightarrow x+10=0\)

\(\Rightarrow x=-10\)

cộng 3 vào cả hai vế nên phương trình vẫn bằng nhau

Ta có \(\frac{x+1}{9}+1+\frac{x+4}{6}+1+\frac{x+5}{5}+1=\frac{x+2}{8}+1+\frac{x+3}{7}+1+\frac{x+6}{4}+1\)

\(\Leftrightarrow\frac{x+10}{9}+\frac{x+10}{6}+\frac{x+10}{5}=\frac{x+10}{8}+\frac{x+10}{7}+\frac{x+10}{4}\)

\(\Leftrightarrow\frac{x+10}{9}+\frac{x+10}{6}+\frac{x+10}{5}-\frac{x+10}{8}-\frac{x+10}{7}-\frac{x+10}{4}=0\)

\(\Leftrightarrow\left(x+10\right)\left(\frac{1}{9}+\frac{1}{6}+\frac{1}{5}-\frac{1}{8}-\frac{1}{7}-\frac{1}{6}\right)=0\)

mà \(\frac{1}{9}+\frac{1}{6}+\frac{1}{5}-\frac{1}{8}-\frac{1}{7}-\frac{1}{6}\ne0\)

\(\Rightarrow x+10=0\)

\(\Leftrightarrow x=-10\)

tự làm để nc trí óc dễ

= \(x^8.\frac{1}{10}.\frac{2}{9}.\frac{3}{8}.\frac{4}{7}.\frac{5}{6}.\frac{6}{5}.\frac{7}{4}.\frac{8}{3}.\frac{9}{2}\)

= \(x^8.\frac{1}{10}.\left(\frac{2}{9}.\frac{9}{2}\right).\left(\frac{3}{8}.\frac{8}{3}\right).\left(\frac{4}{7}.\frac{7}{4}\right).\left(\frac{5}{6}.\frac{6}{5}\right)\)

= \(x^8.\frac{1}{10}.1.1.1.1\)

= \(x^8.\frac{1}{10}\)

Mk ko pik co dung ko nua

=4/10

\(\frac{x^8}{10}\)

Không biết đề làm sao mình làm được đây

#)Giải :

a) x + 2x + 3x + ... + 100x = - 213

=> 100x + ( 2 + 3 + 4 + ... + 100 ) = - 213 

=> 100x + 5049 = - 213 

<=> 100x = - 5262

<=> x = - 52,62

#)Giải :

b) \(\frac{1}{2}x-\frac{1}{3}=\frac{1}{4}x-\frac{1}{6}\)

\(\Rightarrow\frac{1}{2}x+\frac{1}{4}x=\frac{1}{3}+\frac{1}{6}\)

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

\(\Rightarrow\left(\frac{1}{2}+\frac{1}{4}\right)x=\frac{1}{2}\)

\(\Rightarrow\frac{3}{4}x=\frac{1}{2}\)

\(\Leftrightarrow x=\frac{2}{3}\)

a) x + 2x + 3x + ... +100x = -213

=>  x . (1 + 2 + 3 +... + 100) = - 213

=> x . 5050 = -213

=> x           = - 213 : 5050

=> x           = -213/5050

b) \(\frac{1}{2}x-\frac{1}{3}=\frac{1}{4}x-\frac{1}{6}\)

=> \(\frac{1}{2}x-\frac{1}{4}x=\frac{1}{3}-\frac{1}{6}\)

=> \(x.\left(\frac{1}{2}-\frac{1}{4}\right)=\frac{1}{6}\)

=> \(x.\frac{1}{4}=\frac{1}{6}\)

=> \(x=\frac{1}{6}:\frac{1}{4}\)

=> \(x=\frac{2}{3}\)

c) 3(x-2) + 2(x-1) = 10

=> 3x - 6 + 2x - 2 = 10

=> 3x + 2x - 6 - 2 = 10

=> 5x - 8 = 10

=> 5x = 10 + 8

=> 5x = 18

=> x = 18:5

=> x = 3,6

d) \(\frac{x+1}{3}=\frac{x-2}{4}\)

=> \(4\left(x+1\right)=3\left(x-2\right)\)

=>\(4x+4=3x-6\)

=> \(4x-3x=-4-6\)

=> \(x=-10\)

\(\frac{x+1}{10}+\frac{x+2}{9}+\frac{x+3}{8}+\frac{x+4}{7}+\frac{x+5}{6}=-5\)

\(\left(\frac{x+1}{10}+1\right)+\left(\frac{x+2}{9}+1\right)+\left(\frac{x+3}{8}+1\right)+\left(\frac{x+4}{7}+1\right)+\left(\frac{x+5}{6}+1\right)=0\)

\(\frac{x+11}{10}+\frac{x+11}{9}+\frac{x+11}{8}+\frac{x+11}{7}+\frac{x+12}{6}=0\)

\(\left(x+11\right)\left(\frac{1}{10}+\frac{1}{9}+\frac{1}{8}+\frac{1}{7}+\frac{1}{6}\right)=0\)

Vì : \(\frac{1}{10}+\frac{1}{9}+\frac{1}{8}+\frac{1}{7}+\frac{1}{6}>0\)

\(\Rightarrow x+11=0\)

\(\Rightarrow x=-11\)

\(\Leftrightarrow\frac{x+4}{9}+\frac{x+11}{8}+\frac{x+16}{7}+\frac{x+19}{6}=10\)

\(\Leftrightarrow\left(\frac{x+4}{9}-1\right)+\left(\frac{x+11}{8}-2\right)+\left(\frac{x+16}{7}-3\right)+\left(\frac{x+19}{6}-4\right)=0\)

\(\Leftrightarrow\frac{x+4-9}{9}+\frac{x+11-16}{8}+\frac{x+16-21}{7}+\frac{x+19-24}{6}=0\)

\(\Leftrightarrow\frac{x-5}{9}+\frac{x-5}{8}+\frac{x-5}{7}+\frac{x-5}{6}=0\)

\(\Leftrightarrow\left(x-5\right)\left(\frac{1}{9}+\frac{1}{8}+\frac{1}{7}+\frac{1}{6}\right)=0\)

\(\Leftrightarrow x-5=0\)

\(\Leftrightarrow x=5\)

V...

1)

\(2\frac{1}{4}x-9\frac{1}{4}=-7\frac{1}{4}\)

\(2\frac{1}{4}x=\left(-7\frac{1}{4}\right)+9\frac{1}{4}\)

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

\(x=2:2\frac{1}{4}\)

\(x=\frac{8}{9}\)

Vậy \(x=\frac{8}{9}\)

(x+2)/17+(x+4)/15+(x+6)/13=(x+8)/11+(x+10)/9+(x+12)/7

=>(x+2+17)/17+(x+4+15)/15+(x+6+13)/13=(x+8+11)/11+(x+10+9)/9+(x+12+7)/7

=>(x+19)/17+(x+19)/15+(x+19)/13=(x+19)/11+(x+19)/9+(x+19)/7

=>(x+19)/17+(x+19)/15+(x+19)/13-(x+19)/11-(x+19)/9-(x+19)/7=0

=>(x+19)*(1/17+1/15+1/13-1/11-1/9-1/7)=0

=>x+19=0

=>x=19

áp dụng tc tỉ lệ thức ta có :

\(\Leftrightarrow\frac{671x+2804}{3315}=\frac{239x+2462}{693}\Rightarrow\left(671x+2804\right)693=3315\left(239x+2462\right)\)

=>(671x+2804)693=693(671x+2804) (VT)

<=>693(671x+2804)=3315(239x+2462)

=>465003x+1943172=792285x+8161530

=>-327282x=621835

=>x=621835:(-327282)

=>x=-19