\(\frac{1}{x^2+3}+\frac{1}{x^2+9x+18}+\frac{1}{x^2+15x+54}=\frac{1}{2}\left(27-\frac{1}{x+9}\right)\)

\(\Leftrightarrow\frac{3}{x\left(x+3\right)}+\frac{3}{\left(x+3\right)\left(x+6\right)}+\frac{3}{\left(x+6\right)\left(x+9\right)}=27-\frac{1}{x+9}\)

Mà 

\(\frac{3}{x\left(x+3\right)}+\frac{3}{\left(x+3\right)\left(x+6\right)}+\frac{3}{\left(x+6\right)\left(x+9\right)}\)

\(=\frac{1}{x}-\frac{1}{x+3}+\frac{1}{x+3}-\frac{1}{x+6}+\frac{1}{x+6}-\frac{1}{x+9}\)

\(=\frac{1}{x}-\frac{1}{x+9}\)

\(\Rightarrow\frac{1}{x}=27\Rightarrow x=\frac{1}{27}\)

1)

a)

\(\frac{-5}{6}.\frac{120}{25}< x< \frac{-7}{15}.\frac{9}{14}\)

\(\frac{-1}{1}.\frac{20}{5}< x< \frac{-1}{5}.\frac{3}{2}\)

\(\frac{-20}{5}< x< \frac{-3}{10}\)

\(\frac{-40}{10}< x< \frac{-3}{10}\)

\(\Rightarrow Z\in\left\{-4;-5;-6;-7;-8;-9;-10;...;-39\right\}\)

\(\left(\frac{-5}{3}\right)^3< x< \frac{-24}{35}.\frac{-5}{6}\)

\(\frac{25}{3}< x< \frac{-4}{7}.\frac{1}{1}\)

\(\frac{-25}{3}< x< \frac{-4}{7}\)

\(\frac{-175}{21}< x< \frac{-12}{21}\)

\(\Rightarrow Z\in\left\{-13;-14;-15;-16;...;-174\right\}\)

2)

a)

\(\left(\frac{9}{10}-\frac{15}{16}\right).\left(\frac{5}{12}-\frac{11}{15}-\frac{7}{20}\right)\)

\(=\left(\frac{72}{80}-\frac{75}{80}\right).\left(\frac{25}{60}-\frac{44}{60}-\frac{21}{60}\right)\)

\(=\frac{-3}{80}.\frac{-40}{60}\)

\(=\frac{-1}{-2}.\frac{-1}{-20}\)

\(=\frac{1}{40}\)

\(\left(4\frac{46}{65}+x\right).1\frac{1}{12}=5,75\)

\(\Rightarrow\frac{306}{65}+x.\frac{13}{12}=\frac{23}{4}\)

\(\Rightarrow\frac{51}{10}+\frac{13}{12}x=\frac{23}{4}\)

\(\Rightarrow306x=65x=345\)

\(\Rightarrow65x=39\)

\(\Rightarrow x=\frac{3}{5}\)

b, \(\frac{5}{4}-\left(\frac{3}{2}x+0,5\right)=1\frac{1}{4}\)

\(\Rightarrow\frac{5}{4}-\frac{3}{2}x-0,5=\frac{5}{4}\)

\(\Rightarrow\frac{5}{4}-\frac{3}{2}x-\frac{1}{2}=\frac{5}{4}\)

\(\Rightarrow\frac{3}{4}-\frac{3}{2}x=\frac{5}{4}\)

\(\Rightarrow3-6x=5\)

\(\Rightarrow-6x=2\)

\(\Rightarrow x=-\frac{1}{3}\)

mai bn pai đi hok a

lê phạm anh thư Học thêm nha...

thé ak

Dễ mà

a, \(\left(4\frac{46}{65}+x\right).1\frac{1}{2}=5,75\)

\(\left(4\frac{46}{65}+x\right)=5,75:1\frac{1}{2}\)

\(\left(4\frac{46}{65}.x\right)=4\)

\(x=4:4\frac{46}{65}\)

\(x=\frac{130}{153}\)

b tương tự

a,(\(4\frac{46}{65}\)+ x).\(1\frac{1}{12}\)= 5,75

(\(\frac{306}{65}\)+x).\(\frac{13}{12}\)=5,75

(\(\frac{306}{65}\)+x)          = 5,75 / \(\frac{13}{12}\)

(\(\frac{306}{65}\)+x)          = \(\frac{69}{13}\)

                 x            = \(\frac{69}{13}\)- \(\frac{306}{65}\)

                 x            = \(\frac{3}{5}\)

a)  \(=\frac{1}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}.\frac{5.5}{4.6}.\frac{6.6}{5.7}=\frac{6}{2.7}=\frac{3}{7}\)

B) \(=\frac{70}{11}+\frac{1}{9}-\frac{37}{11}-\frac{1}{9}=\left(\frac{70}{11}-\frac{37}{11}\right)+\left(\frac{1}{9}-\frac{1}{9}\right)=\frac{33}{11}+0=3\)

BÀI 2:

A) \(\Leftrightarrow\frac{7}{2}x-\frac{x}{2}+\frac{2x}{2}=\frac{7}{2}.\frac{5}{6}\)

\(\Leftrightarrow\frac{7x-x+2x}{2}=\frac{35}{12}\)

\(\Leftrightarrow\frac{8x}{2}=\frac{35}{12}\)

\(\Leftrightarrow8x.12=35.2\Leftrightarrow96x=70\Leftrightarrow x=\frac{70}{96}=\frac{35}{48}\)

b) \(\left(x-\frac{3}{1.2}\right)+\left(x-\frac{3}{2.3}\right)+...+\left(x-\frac{3}{99.100}\right)=1\)

\(x-\frac{3}{1.2}+x-\frac{3}{2.3}+....x+\frac{3}{99.100}=1\)

\(\Leftrightarrow\left(x+x+x+...+x\right)-3\left(\frac{1}{1.2}+\frac{1}{1.3}+....+\frac{1}{99.100}\right)=1\)

ngoặc 1 có 99 số hạng x

\(\Leftrightarrow99x-3\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{99}-\frac{1}{100}\right)=1\)

\(\Leftrightarrow99x-3\left(1-\frac{1}{100}\right)=1\)

\(\Leftrightarrow99x-3.\frac{99}{100}=1\)

\(\Leftrightarrow99x=1+\frac{3.99}{100}\)

\(\Leftrightarrow99x=\frac{397}{100}\)

\(\Leftrightarrow x=\frac{397}{100.99}=\frac{397}{9900}\)

\(a,\frac{x+8}{3}+\frac{x+7}{2}=-\frac{x}{5}\)

\(\Leftrightarrow\frac{10\cdot\left(x+8\right)}{30}+\frac{15\left(x+7\right)}{30}=\frac{-6x}{30}\)

\(\rightarrow10x+80+15x+105=-6x\)

\(\Leftrightarrow31x+185=0\)

\(\Leftrightarrow x=-\frac{185}{31}\)

b,\(b,\frac{x-8}{3}+\frac{x-7}{4}=4+\frac{1-x}{5}\)

\(\Leftrightarrow\frac{20\left(x-8\right)}{60}+\frac{15\left(x-7\right)}{60}=\frac{240}{60}+\frac{12\left(1-x\right)}{60}\)

\(\rightarrow20x-160+15x-105=240+12-12x\)

\(\Leftrightarrow47x-517=0\)\(\Leftrightarrow x=11\)

Ko hiểu đề!

\(\left(3\frac{1}{2}+2x\right).2\frac{2}{3}=5\frac{1}{3}\)

<=>\(\left(\frac{7}{2}+2x\right).\frac{8}{3}=\frac{16}{3}\)

<=>\(\frac{28}{3}+\frac{16x}{3}=\frac{16}{3}\)

<=>\(\frac{16x}{3}=\frac{-2}{3}\)

<=>\(16x=-2\)

<=>\(x=\frac{-1}{8}\)

vậy \(x=\frac{-1}{8}\)

b,\(\left|2x+3\right|=5\)

xét x<0,ta co: \(\left|2x+3\right|=5\)<=> \(-2x+3=5\)<=>\(-2x=2\)<=>\(x=-1\)(loại)

xét x>0,ta co:\(\left|2x+3\right|=5\)<=>\(2x+3=5\)<=>\(2x=2\)<=>\(x=1\)

c,\(\frac{x-2}{4}=\frac{5+x}{3}\)

<=>\(\frac{3x-6}{12}=\frac{20+4x}{12}\)

=>\(3x-6=20+4x\)

<=>\(3x-6-20-4x=0\)

<=>\(-x-26=0\)

<=>\(-x=26\)

<=>\(x=-26\)

kl:.......