\(\frac{30x+40}{x}=1500:30\)

\(\frac{30x+40}{x}=50\)

Suy ra 30x+40= 50.x

40= 50x- 30x

40= 20x

x=40:20=2

\(1500:\frac{30x+40}{x}=30\)

\(\frac{30x+40}{x}=1500:30\)

\(\frac{30x+40}{x}=50\)

\(\Rightarrow30x+40=50x\)

\(30x+40-50x=0\)

\(40+\left(30x-50x\right)=0\)

\(40-20x=0\)

\(20\left(20-x\right)=0\)

\(\Rightarrow20-x=0\)

\(x=20\)

Vậy x = 20

x=2 nhoa bạn ! í mà nè,bạn làm sao mà viết được phân số hay dợ

\(3^5\)

Đễ mà sao không tự làm đi

\(\frac{2}{5}+\frac{22}{15}x=\frac{23}{30}\)

\(\frac{22}{15}x=\frac{23}{30}-\frac{2}{5}\)

\(\frac{22}{15}x=\frac{23}{30}-\frac{12}{30}\)

\(\frac{22}{15}x=\frac{11}{30}\)

\(x=\frac{11}{30}:\frac{22}{15}\)

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

Vậy x = \(\frac{1}{4}\)

22/15x = 23/30 - 2/5

22/15x = 11/30

x= 11/30 : 22/15

x= 1/4

\(\frac{5x-1}{10}+\frac{2x+3}{6}=\frac{x-8}{15}-\frac{x}{30}\)

\(\Leftrightarrow3\left(5x-1\right)+5\left(2x+3\right)=2\left(x-8\right)-x\)

\(\Leftrightarrow15x-3+10x+15=2x-16-x\)

\(\Leftrightarrow15x+10x-2x+x=-16+3-15\)

\(\Leftrightarrow24x=-28\)

\(\Leftrightarrow x=\frac{-28}{24}=\frac{-7}{6}\)

Vậy ... 

\(\frac{x-15}{2014}+\frac{x-20}{2019}=\frac{x-5}{2004}+\frac{x+30}{1969}\)

\(\Leftrightarrow\frac{x-15}{2014}+1+\frac{x-20}{2019}+1=\frac{x-5}{2004}+1+\frac{x+30}{1969}+1\)

\(\Leftrightarrow\frac{x-15+2014}{2014}+\frac{x-20+2019}{2019}-\frac{x-5+2004}{2004}-\frac{x+30+1969}{1969}=0\)

\(\Leftrightarrow\frac{x-1999}{2014}+\frac{x+1999}{2019}-\frac{x+1999}{2004}-\frac{x+1999}{1969}=0\)

\(\Leftrightarrow\left(x-1999\right)\left(\frac{1}{2014}+\frac{1}{2019}-\frac{1}{2004}-\frac{1}{1969}\right)=0\)

Vì \(\left(\frac{1}{2014}+\frac{1}{2019}-\frac{1}{2004}-\frac{1}{1969}\right)\ne0\)

nên \(x-1999=0\)

\(\Leftrightarrow x=1999\)

\(easy!\)(sai đề + sửa đề)

\(\frac{x-5}{2014}+\frac{x-20}{2019}-\frac{x-5}{2004}-\frac{x+3}{1969}=0\)

\(\Leftrightarrow\left(\frac{x-15}{2014}-1\right)+\left(\frac{x-20}{2019}-1\right)-\left(\frac{x-5}{2004}-1\right)-\left(\frac{x-30}{1969}-1\right)=0\)

\(\Leftrightarrow\frac{x-1999}{2014}+\frac{x-1999}{2019}-\frac{x-1999}{2004}-\frac{x-1999}{1969}=0\)

\(\Leftrightarrow\left(x-1999\right)\left(\frac{1}{2014}+\frac{1}{2019}-\frac{1}{2004}-\frac{1}{1969}\right)=0\)

dễ dàng cm được \(x-1999=0\)

\(\Leftrightarrow x=1999\)

          \(\frac{x+1999}{2014}-1+\frac{x+1999}{2019}-1=\frac{x+1999}{2004}-1+\frac{x+1999}{1969}\)

<=>   \(\frac{x+1999}{2014}+\frac{x+1999}{2019}-\frac{x+1999}{2004}-\frac{x+1999}{1969}=0\)

<=> \(\left(x+1999\right)\left(\frac{1}{2014}+\frac{1}{2019}-\frac{1}{2004}-\frac{1}{1969}\right)=0\)

 Vì     \(\frac{1}{2014}+\frac{1}{2014}-\frac{1}{2004}-\frac{1}{1969}\)khác 0 (tự c/m)

  => x+1999=0

  => x=-1999

     Vậy x=-1999 thì ......

\(x-\frac{3.\left(x+30\right)}{15}-24\frac{1}{2}=\frac{7x}{10}-\frac{2.\left(10x+2\right)}{5}\)

\(\Leftrightarrow\frac{x}{1}-\frac{3x+90}{15}-\frac{49}{2}=\frac{7x}{10}-\frac{20x+4}{5}\)

\(\Leftrightarrow\frac{30x}{30}-\frac{2.\left(3x+90\right)}{15.2}-\frac{49.15}{2.15}=\frac{7x.3}{10.3}-\frac{6.\left(20x+4\right)}{6.5}\)

\(\Leftrightarrow\frac{30x}{30}-\frac{6x+180}{30}-\frac{735}{30}=\frac{21x}{30}-\frac{120x+24}{30}\)

\(\Rightarrow30x-\left(6x+180\right)-735=21x-\left(120x+24\right)\)

\(\Leftrightarrow30x-6x-180-735=21x-120x-24\)

\(\Leftrightarrow24x-915=-99x-24\)

\(\Leftrightarrow24x+99x=-24+915\)

\(\Leftrightarrow123x=891\)

\(\Leftrightarrow x=891:123\)

\(\Leftrightarrow x=\frac{297}{41}.\)

Vậy phương trình có tập hợp nghiệm là: \(S=\left\{\frac{297}{41}\right\}.\)

Chúc bạn học tốt!

x-\(\frac{3\left(x+30\right)}{15}\)-26=\(\frac{7x}{10}\)-\(\frac{2\left(10x+2\right)}{5}\)

➜\(\frac{30x}{30}\)-\(\frac{6\left(x+30\right)}{30}\)-\(\frac{780}{30}\)=\(\frac{21x}{30}\)-\(\frac{12\left(10x+2\right)}{30}\)

➜ 30x-6x-180-780=21x-120x-24

➜30x-6x-21x-120x=780+180-24

➜Bạn tự tính!!!

\(\frac{4^{15}}{7^{30}}=\frac{2^{30}}{7^{30}}\)  và \(\frac{8^{10}.3^{30}}{7^{30}.4^{15}}=\frac{2^{30}.3^{30}}{7^{30}.2^{30}}=\frac{2^{30}}{7^{30}}\)Vậy hai vế bằng nhau