Question

Tìm x:

\(\dfrac{x+32}{11}+\dfrac{x+33}{12}=\dfrac{x+34}{13}+\dfrac{x+35}{14}\)

Answer 1

\(\dfrac{x+32}{11}+\dfrac{x+33}{12}=\dfrac{x+34}{13}+\dfrac{x+35}{14}\)

\(\Leftrightarrow\left(\dfrac{x+32}{11}-1\right)+\left(\dfrac{x+33}{12}-1\right)=\left(\dfrac{x+34}{13}-1\right)+\left(\dfrac{x+35}{14}-1\right)\)

\(\Leftrightarrow\dfrac{x+21}{11}+\dfrac{x+21}{12}=\dfrac{x+21}{13}+\dfrac{x+21}{14}\)

\(\Leftrightarrow\dfrac{x+21}{11}+\dfrac{x+21}{12}-\dfrac{x+21}{13}-\dfrac{x+21}{14}=0\)

\(\Leftrightarrow\left(x+21\right)\left(\dfrac{1}{11}+\dfrac{1}{12}-\dfrac{1}{13}-\dfrac{1}{14}\right)=0\)

Mà \(\dfrac{1}{11}+\dfrac{1}{12}-\dfrac{1}{13}-\dfrac{1}{14}\ne0\)

\(\Leftrightarrow x+21=0\)

\(\Leftrightarrow x=-21\)

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