pt \(\Leftrightarrow\left(\dfrac{x+16}{49}+1\right)+\left(\dfrac{x+18}{47}+1\right)=\left(\dfrac{x+20}{45}+1\right)\)
\(\Leftrightarrow\dfrac{x+65}{49}+\dfrac{x+65}{47}-\dfrac{x+65}{45}=0\)
\(\Leftrightarrow\left(x+65\right)\left(\dfrac{1}{49}+\dfrac{1}{47}-\dfrac{1}{45}\right)=0\)
\(\Leftrightarrow x+65=0\)
\(\Leftrightarrow x=-65\)
\(\dfrac{x+16}{49}+\dfrac{x+18}{47}=\dfrac{x+20}{45}+1\left(1\right)\)
Thêm (2) vào vế của p.trình (1) ta có :
\(\Leftrightarrow\dfrac{x+16}{49}+1+\dfrac{x+18}{47}+1=\dfrac{x+20}{45}+1\)
\(\Leftrightarrow\dfrac{x+65}{49}+\dfrac{x+65}{47}-\dfrac{x+65}{45}=0\) (2)
\(\Leftrightarrow\left(x+65\right)\left(\dfrac{1}{49}+\dfrac{1}{47}-\dfrac{1}{45}\right)=0\)
\(\Leftrightarrow x+65=0\) ( vì \(\dfrac{1}{49}+\dfrac{1}{47}-\dfrac{1}{45}\ne0\))
\(\Leftrightarrow x=-65\)