a: \(\dfrac{x+2}{98}+\dfrac{x+4}{96}=\dfrac{x+6}{94}+\dfrac{x+8}{92}\)
=>\(\dfrac{x+2}{98}+1+\dfrac{x+4}{96}+1=\dfrac{x+6}{94}+1+\dfrac{x+8}{92}+1\)
=>\(\dfrac{x+100}{98}+\dfrac{x+100}{96}-\dfrac{x+100}{94}-\dfrac{x+100}{92}=0\)
=>\(\left(x+100\right)\left(\dfrac{1}{98}+\dfrac{1}{96}-\dfrac{1}{94}-\dfrac{1}{92}\right)=0\)
=>x+100=0
=>x=-100
b: \(\dfrac{x-214}{86}+\dfrac{x-132}{84}+\dfrac{x-54}{82}=6\)
=>\(\left(\dfrac{x-214}{86}-1\right)+\left(\dfrac{x-132}{84}-2\right)+\left(\dfrac{x-54}{82}-3\right)=0\)
=>\(\dfrac{x-300}{86}+\dfrac{x-300}{84}+\dfrac{x-300}{82}=0\)
=>x-300=0
=>x=300
c: \(\dfrac{148-x}{25}+\dfrac{169-x}{23}+\dfrac{186-x}{21}+\dfrac{199-x}{19}=10\)
=>\(\left(\dfrac{148-x}{25}-1\right)+\left(\dfrac{169-x}{23}-2\right)+\left(\dfrac{186-x}{21}-3\right)+\left(\dfrac{199-x}{19}-4\right)=0\)
=>\(\dfrac{123-x}{25}+\dfrac{123-x}{23}+\dfrac{123-x}{21}+\dfrac{123-x}{19}=0\)
=>123-x=0
=>x=123
d: \(\dfrac{x-17}{1990}+\dfrac{x-21}{1986}+\dfrac{x+1}{1004}=4\)
=>\(\dfrac{x-17}{1990}-1+\dfrac{x-21}{1986}-1+\dfrac{x+1}{1004}-2=0\)
=>\(\dfrac{x-2007}{1990}+\dfrac{x-2007}{1986}+\dfrac{x-2007}{1004}=0\)
=>x-2007=0
=>x=2007
a) \(\dfrac{x+2}{98}+\dfrac{x+4}{96}=\dfrac{x+6}{94}+\dfrac{x+8}{92}\)
\(\Leftrightarrow\dfrac{x+2}{98}+\dfrac{x+4}{96}-\dfrac{x+6}{94}-\dfrac{x+8}{92}=0\)
\(\Leftrightarrow\left(\dfrac{x+2}{98}+1\right)+\left(\dfrac{x+4}{96}+1\right)-\left(\dfrac{x+6}{94}+1\right)-\left(\dfrac{x+8}{92}+1\right)=0\)
\(\Leftrightarrow\dfrac{x+100}{98}+\dfrac{x+100}{96}-\dfrac{x+100}{94}-\dfrac{x+100}{92}=0\)
\(\Leftrightarrow\left(x+100\right)\left(\dfrac{1}{98}+\dfrac{1}{96}-\dfrac{1}{94}-\dfrac{1}{92}\right)=0\)
\(\Leftrightarrow x+100=0\) (vì \(\dfrac{1}{98}+\dfrac{1}{96}-\dfrac{1}{94}-\dfrac{1}{92}\ne0\))
\(\Leftrightarrow x=-100\)
b) \(\dfrac{x-214}{86}+\dfrac{x-132}{84}+\dfrac{x-54}{82}=6\)
\(\Leftrightarrow\left(\dfrac{x-214}{86}-1\right)+\left(\dfrac{x-132}{84}-2\right)+\left(\dfrac{x-54}{82}-3\right)=0\)
\(\Leftrightarrow\dfrac{x-300}{86}+\dfrac{x-300}{84}+\dfrac{x-300}{82}=0\)
\(\Leftrightarrow\left(x-300\right)\left(\dfrac{1}{86}+\dfrac{1}{84}+\dfrac{1}{82}\right)=0\)
\(\Leftrightarrow x-300=0\) (vì \(\dfrac{1}{86}+\dfrac{1}{84}+\dfrac{1}{82}\ne0\))
\(\Leftrightarrow x=300\)
c) \(\dfrac{148-x}{25}+\dfrac{169-x}{23}+\dfrac{186-x}{21}+\dfrac{199-x}{19}=10\)
\(\Leftrightarrow\left(\dfrac{148-x}{25}-1\right)+\left(\dfrac{169-x}{23}-2\right)+\left(\dfrac{186-x}{21}-3\right)+\left(\dfrac{199-x}{19}-4\right)=0\)
\(\Leftrightarrow\dfrac{123-x}{25}+\dfrac{123-x}{23}+\dfrac{123-x}{21}+\dfrac{123-x}{19}=0\)
\(\Leftrightarrow\left(123-x\right)\left(\dfrac{1}{25}+\dfrac{1}{23}+\dfrac{1}{21}+\dfrac{1}{19}\right)=0\)
\(\Leftrightarrow123-x=0\) (vì \(\dfrac{1}{25}+\dfrac{1}{23}+\dfrac{1}{21}+\dfrac{1}{19}\ne0\))
\(\Leftrightarrow x=123\)
d) \(\dfrac{x-17}{1990}+\dfrac{x-21}{1986}+\dfrac{x+1}{1004}=4\)
\(\Leftrightarrow\left(\dfrac{x-17}{1990}-1\right)+\left(\dfrac{x-21}{1986}-1\right)+\left(\dfrac{x+1}{1004}-2\right)=0\)
\(\Leftrightarrow\dfrac{x-2007}{1990}+\dfrac{x-2007}{1986}+\dfrac{x-2007}{1004}=0\)
\(\Leftrightarrow\left(x-2007\right)\left(\dfrac{1}{1990}+\dfrac{1}{1986}+\dfrac{1}{1004}\right)=0\)
\(\Leftrightarrow x-2007=0\) (vì \(\dfrac{1}{1990}+\dfrac{1}{1986}+\dfrac{1}{1004}\ne0\))
\(\Leftrightarrow x=2007\)
$Toru$
