Giải:

Ta có: \(\frac{201-x}{99}+\frac{205-x}{95}+\frac{203-x}{97}+3=0\)

\(\Leftrightarrow\frac{201-x}{99}+1+\frac{205-x}{95}+1+\frac{203-x}{97}+1=0\)

\(\Leftrightarrow\frac{300-x}{99}+\frac{300-x}{95}+\frac{300-x}{97}=0\)

\(\Leftrightarrow\left(300-x\right)\left(\frac{1}{99}+\frac{1}{95}+\frac{1}{97}\right)=0\)

\(\Leftrightarrow300-x=0\) (Vì \(\frac{1}{99}+\frac{1}{95}+\frac{1}{97}\ne0\))

\(\Leftrightarrow x=300\)

Vậy phương trình có nghiệm là \(x=300.\)

Chúc bạn học tốt@@

`(201-x)/99+(203-x)/97+(205-x)/95+3=0`

`<=>(201-x)/99+1+(203-x)/97+1+(205-x)/95+1=0`

`<=>(300-x)/99+(300-x)/97+(300-x)/95=0`

`<=>(300-x)(1/99+1/97+1/95)=0`

`<=>300-x=0`

`<=>x=300`

Vậy `x=300`

Sai đề.

\(\Leftrightarrow\left(\dfrac{201-x}{99}+1\right)+\left(\dfrac{203-x}{97}+1\right)+\left(\dfrac{205-x}{95}+1\right)=0\)

=>300-x=0

=>x=300

<=> 300-x/99+300-x/97+300-x/95=0

<=>(300-x).(1/99+1/97+1/95)=0

<=>300-x=0

<=>x=300

Sửa đề: \(\dfrac{201-x}{99}+\dfrac{203-x}{97}+\dfrac{205-x}{95}+3=0\)

Ta có: \(\dfrac{201-x}{99}+\dfrac{203-x}{97}+\dfrac{205-x}{95}+3=0\)

\(\Leftrightarrow\dfrac{201-x}{99}+1+\dfrac{203-x}{97}+1+\dfrac{205-x}{95}+1=0\)

\(\Leftrightarrow\dfrac{300-x}{99}+\dfrac{300-x}{97}+\dfrac{300-x}{95}=0\)

\(\Leftrightarrow\left(300-x\right)\left(\dfrac{1}{99}+\dfrac{1}{97}+\dfrac{1}{95}\right)=0\)

mà \(\dfrac{1}{99}+\dfrac{1}{97}+\dfrac{1}{95}>0\)

nên 300-x=0

hay x=300

Vậy:S={300}

✔

a) \(\dfrac{x+1}{2004}+\dfrac{x+2}{2003}=\dfrac{x+3}{2002}+\dfrac{x+4}{2001}\) 

⇔ \(\dfrac{x+1}{2004}+1+\dfrac{x+2}{2003}+1=\dfrac{x+3}{2002}+1+\dfrac{x+4}{2001}+1\)

⇔ \(\dfrac{x+2005}{2004}+\dfrac{x+2005}{2003}=\dfrac{x+2005}{2002}+\dfrac{x+2005}{2001}\)

⇔ \(\left(x+2005\right)\left(\dfrac{1}{2004}+\dfrac{1}{2003}-\dfrac{1}{2002}-\dfrac{1}{2001}\right)\)=0

Vì\(\left(\dfrac{1}{2004}+\dfrac{1}{2003}-\dfrac{1}{2002}-\dfrac{1}{2001}\right)\)<0 nên phương trinh đã cho tương đương:

x+2005=0 ⇔x=-2005

b) \(\dfrac{201-x}{99}+\dfrac{203-x}{97}+\dfrac{205-x}{95}+3=0\) 

⇔ \(\dfrac{201-x}{99}+1+\dfrac{203-x}{97}+1+\dfrac{205-x}{95}+1=0\)

⇔ \(\dfrac{300-x}{99}+\dfrac{300-x}{97}+\dfrac{300-x}{95}=0\)

⇔ \(\left(300-x\right)\left(\dfrac{1}{99}+\dfrac{1}{97}+\dfrac{1}{95}\right)=0\)

Vì \(\left(\dfrac{1}{99}+\dfrac{1}{97}+\dfrac{1}{95}\right)>0\) nên phương trình đã cho tương đương:

300-x=0 ⇔ x=300