Question

\(\dfrac{x+8}{1092}+\dfrac{x+10}{1094}=\dfrac{x+12}{1096}+\dfrac{x+14}{1098}\)

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Answer 1

\(\dfrac{x+8}{1092}+\dfrac{x+10}{1094}=\dfrac{x+12}{1096}+\dfrac{x+14}{1098}\)

\(\Leftrightarrow\left(\dfrac{x+8}{1092}-1\right)+\left(\dfrac{x+10}{1094}-1\right)\)\(=\left(\dfrac{x+12}{1096}-1\right)+\left(\dfrac{x+14}{1098}-1\right)\)

\(\Leftrightarrow\dfrac{x-1084}{1092}+\dfrac{x-1084}{1094}=\dfrac{x-1084}{1096}+\dfrac{x-1084}{1098}\)

\(\Leftrightarrow\dfrac{x-1084}{1092}+\dfrac{x-1084}{1094}-\dfrac{x-1084}{1096}-\dfrac{x-1084}{1098}=0\)

\(\Leftrightarrow\left(x-1084\right).\left(\dfrac{1}{1092}+\dfrac{1}{1094}-\dfrac{1}{1096}-\dfrac{1}{1098}\right)=0\)

\(\Rightarrow x-1084=0\Rightarrow x=1084\)

Vậy x=1084