Question

\(\frac{x-4}{100}\)+ \(\frac{x-4}{102}\)= \(\frac{x-4}{103}\)- \(\frac{x-4}{104}\)

Answer 1

(x-4)(1/100+1/102-1/103-1/04)=0

=>x-4=0

=> x=4

Answer 2

\(\left(x-4\right)\left(\frac{1}{100}+\frac{1}{102}-\frac{1}{103}-\frac{1}{104}\right)=0\)

\(\Rightarrow x-4=0\)

\(\Rightarrow4-4=0\)

\(\Rightarrow x=4\)

Answer 3

\(\frac{x-4}{100}+\frac{x-4}{101}=\frac{x-4}{103}+\frac{x-4}{104}\)

=> \(\left(\frac{x-4}{100}+\frac{x-4}{102}\right)-\left(\frac{x-4}{103}+\frac{x-4}{104}\right)=0\)

=> \(\frac{x-4}{100}+\frac{x-4}{102}-\frac{x-4}{103}-\frac{x-4}{104}=0\)

=> \(\left(x-4\right).\left(\frac{1}{100}+\frac{1}{102}-\frac{1}{103}-\frac{1}{104}\right)=0\)

Vì \(\frac{1}{100}>\frac{1}{103};\frac{1}{102}>\frac{1}{104}\)

=> \(\frac{1}{100}+\frac{1}{102}-\frac{1}{103}-\frac{1}{104}\ne0\)

=> x - 4 = 0

=> x = 0 + 4

=> x = 4

Vậy x = 4

Answer 4

\(\frac{x-4}{100}+\frac{x-4}{101}=\frac{x-4}{103}+\frac{x-4}{104}\)

\(\Rightarrow\left(\frac{x-4}{100}+\frac{x-4}{102}\right)-\left(\frac{x-4}{103}+\frac{x-4}{104}\right)=0\)

\(\Rightarrow\frac{x-4}{100}+\frac{x-4}{102}-\frac{x-4}{103}-\frac{x-4}{104}=0\)

\(\Rightarrow\left(x-4\right).\left(\frac{1}{100}+\frac{1}{102}-\frac{1}{103}-\frac{1}{104}\right)=0\)

\(\text{Vì }\)\(\frac{1}{100}>\frac{1}{103};\frac{1}{102}>\frac{1}{104}\)

\(\Rightarrow\frac{1}{100}+\frac{1}{102}-\frac{1}{103}-\frac{1}{104}\ne0\)

=> x - 4 = 0

=> x = 0 + 4

=> x = 4

Vậy x = 4