Question

Giải phương trình giúp mình:

(x+5)/(105)+(x+1)/(109)=-(x+113)/(3)-(x+117)/(7)

 

Answer 1

          \(\frac{x+5}{105}+\frac{x+1}{109}=-\frac{x+113}{3}-\frac{x+117}{7}\)

\(\Leftrightarrow\)\(\frac{x+5}{105}+1+\frac{x+1}{109}+1=-\frac{x+113}{3}+1-\frac{x+117}{7}+1\)

\(\Leftrightarrow\)\(\frac{x+110}{105}+\frac{x+110}{109}=-\frac{x+110}{3}-\frac{x+110}{7}\)

\(\Leftrightarrow\)\(\frac{x+110}{105}+\frac{x+110}{109}+\frac{x+110}{3}+\frac{x+110}{7}=0\)

\(\Leftrightarrow\)\(\left(x+110\right)\left(\frac{1}{105}+\frac{1}{109}+\frac{1}{3}+\frac{1}{7}\right)=0\)

\(\Leftrightarrow\)\(x+110=0\)  (do  1/105 + 1/109 + 1/3 + 1/7 # 0)

\(\Leftrightarrow\)\(x=-110\)

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