Question

giải chi tiết nha

Answer 1

a: \(\dfrac{x-5}{100}+\dfrac{x-4}{101}+\dfrac{x-3}{102}=\dfrac{x-100}{5}+\dfrac{x-101}{4}+\dfrac{x-102}{3}\)

=>\(\left(\dfrac{x-5}{100}-1\right)+\left(\dfrac{x-4}{101}-1\right)+\left(\dfrac{x-3}{102}-1\right)=\left(\dfrac{x-100}{5}-1\right)+\left(\dfrac{x-101}{4}-1\right)+\left(\dfrac{x-102}{3}-1\right)\)

=>\(\dfrac{x-105}{100}+\dfrac{x-105}{101}+\dfrac{x-105}{102}-\dfrac{x-105}{5}-\dfrac{x-105}{4}-\dfrac{x-105}{3}=0\)

=>x-105=0

=>x=105

b: \(\dfrac{x-2}{7}+\dfrac{x-1}{8}=\dfrac{x-4}{5}+\dfrac{x-3}{6}\)

=>\(\left(\dfrac{x-2}{7}-1\right)+\left(\dfrac{x-1}{8}-1\right)=\left(\dfrac{x-4}{5}-1\right)+\left(\dfrac{x-3}{6}-1\right)\)

=>\(\dfrac{x-9}{7}+\dfrac{x-9}{8}-\dfrac{x-9}{5}-\dfrac{x-9}{6}=0\)

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

=>x-9=0

=>x=9

c: \(\dfrac{x-103}{100}+\dfrac{x-205}{101}+\dfrac{x+303}{102}=0\)

=>\(\left(\dfrac{x-103}{100}+1\right)+\left(\dfrac{x-205}{101}+2\right)+\left(\dfrac{x+303}{102}-3\right)=0\)

=>\(\dfrac{x-3}{100}+\dfrac{x-3}{101}+\dfrac{x-3}{102}=0\)

=>x-3=0

=>x=3