Question

Giải phương trình sau:

\(\dfrac{x-2}{102}+\dfrac{x-3}{103}=\dfrac{x-4}{104}+\dfrac{x-5}{105}\)

Answer 1

\(\dfrac{x-2}{102}+\dfrac{x-3}{103}=\dfrac{x-4}{104}+\dfrac{x-5}{105}\)

\(\Leftrightarrow\dfrac{x-2}{102}+1+\dfrac{x-3}{103}+1=\dfrac{x-4}{104}+1+\dfrac{x-5}{105}+1\)

\(\Leftrightarrow\dfrac{x+100}{102}+\dfrac{x+100}{103}-\dfrac{x+100}{104}-\dfrac{x+100}{105}=0\)

\(\Leftrightarrow\left(x+100\right)\left(\dfrac{1}{102}+\dfrac{1}{103}-\dfrac{1}{104}-\dfrac{1}{105}\right)=0\)

\(\Leftrightarrow x+100=0\Leftrightarrow x=-100\)