7/ \(\dfrac{148-x}{25}+\dfrac{169-x}{23}+\dfrac{186-x}{21}+\dfrac{199-x}{19}=10\)
\(\dfrac{148-x}{25}-1+\dfrac{169-x}{23}-2+\dfrac{186-x}{21}-3+\dfrac{199-x}{19}-4=0\)
\(\dfrac{123-x}{25}+\dfrac{123-x}{23}+\dfrac{123-x}{21}+\dfrac{123-x}{19}=0\)
\(\left(123-x\right)\left(\dfrac{1}{25}+\dfrac{1}{23}+\dfrac{1}{21}+\dfrac{1}{19}\right)=0\)
Vì \(\dfrac{1}{25}+\dfrac{1}{23}+\dfrac{1}{21}+\dfrac{1}{19}\ne0\)
=> 123-x=0
x=123
8/\(\dfrac{1}{x-1}-\dfrac{1}{x-2}-\dfrac{1}{x-3}+\dfrac{1}{x-4}=0\) ĐKXĐ: \(\left\{{}\begin{matrix}x\ne1\\x\ne2\\x\ne3\\x\ne4\end{matrix}\right.\)
\(\dfrac{1}{x-1}+\dfrac{1}{x-4}-\dfrac{1}{x-2}-\dfrac{1}{x-3}=0\)
\(\dfrac{2x-5}{\left(x-1\right)\left(x-4\right)}-\dfrac{2x-5}{\left(x-2\right)\left(x-3\right)}=0\)
\(\left(2x-5\right)\left(\dfrac{1}{\left(x-1\right)\left(x-4\right)}-\dfrac{1}{\left(x-2\right)\left(x-3\right)}\right)=0\)
=> 2x-5=0 hoặc \(\dfrac{1}{\left(x-1\right)\left(x-4\right)}-\dfrac{1}{\left(x-2\right)\left(x-3\right)}=0\)
2x=5 \(\dfrac{x^2-5x+6-x^2+5x-4}{\left(x-1\right)\left(x-2\right)\left(x-3\right)\left(x-4\right)}=0\)
\(x=\dfrac{5}{2}\) \(\dfrac{2}{\left(x-1\right)\left(x-2\right)\left(x-3\right)\left(x-4\right)}=0\)
=> 2=0 (vô lí)
