x+1/3+x+14/43+x+1/19+x+26=0

4x+65470/2451=0

4x=-65470/2451

x=-32735/4902

\(\frac{x+10}{30}+\frac{x+14}{43}+\frac{x+5}{95}+\frac{x+130}{5}=0\)

\(\Leftrightarrow\left(\frac{x+10}{30}+3\right)+\left(\frac{x+14}{43}+2\right)+\left(\frac{x+5}{95}+1\right)+\left(\frac{x+130}{5}-6\right)=0\)

\(\Leftrightarrow\frac{x+10+90}{30}+\frac{x+14+86}{43}+\frac{x+5+95}{95}+\frac{x+130-30}{5}=0\)

\(\Leftrightarrow\frac{x+100}{30}+\frac{x+100}{43}+\frac{x+100}{95}+\frac{x+100}{5}=0\)

\(\Leftrightarrow\left(x+100\right)\left(\frac{1}{30}+\frac{1}{43}+\frac{1}{95}+\frac{1}{5}\right)=0\)

Vì \(\frac{1}{30}+\frac{1}{43}+\frac{1}{95}+\frac{1}{5}\ne0\)

=> x + 100 = 0

=> x = -100

Answer:

Có:

\(\frac{x-10}{30}+\frac{x-14}{43}+\frac{x-5}{95}+\frac{x-148}{8}=0\)

\(\Rightarrow\frac{x-10}{30}+\frac{x-14}{43}+\frac{x-5}{95}+\frac{x+100}{8}-6=0\)

\(\Rightarrow\left(\frac{x-10}{30}-3\right)+\left(\frac{x-14}{43}-2\right)+\left(\frac{x-5}{95}-1\right)+\frac{x-100}{8}=0\)

\(\Rightarrow\frac{x-100}{30}+\frac{x-100}{43}+\frac{x-100}{95}+\frac{x-100}{8}=0\)

\(\Rightarrow\left(x-100\right)\left(\frac{1}{30}+\frac{1}{43}+\frac{1}{95}+\frac{1}{9}\right)=0\)

Mà \(\frac{1}{30}+\frac{1}{43}+\frac{1}{95}+\frac{1}{8}\ne0\Leftrightarrow\left(x-100\right)\left(\frac{1}{30}+\frac{1}{43}+\frac{1}{95}+\frac{1}{8}\right)=0\)

\(\Leftrightarrow x-100=0\Leftrightarrow x=100\)

có nhưng có chỗ sai

Sao đang 1/8 lại sang 1/9 lại sang 1/8?

\(\left(\frac{x-10}{30}-3\right)+\left(\frac{x-14}{43}-2\right)+\left(\frac{x-5}{95}-1\right)+\left(\frac{x-148}{8}+6\right)=0\)

\(\Leftrightarrow\left(\frac{x-10}{30}-\frac{90}{30}\right)+\left(\frac{x-14}{43}-\frac{86}{43}\right)+\left(\frac{x-5}{95}-\frac{95}{95}\right)+\left(\frac{x-148}{8}+\frac{48}{8}\right)=0\)

\(\Leftrightarrow\frac{x-100}{30}+\frac{x-100}{43}+\frac{x-100}{95}+\frac{x-100}{8}=0\)

\(\Leftrightarrow\left(x-100\right).\left(\frac{1}{30}+\frac{1}{43}+\frac{1}{95}+\frac{1}{8}\right)=0\)

\(\Rightarrow x-100=0\)( Do \(\frac{1}{30}+\frac{1}{43}+\frac{1}{95}+\frac{1}{8}\ne0\)

=> x=100

\(...\Rightarrow x+x+\dfrac{x}{43}+\dfrac{x}{8}=14+148+\dfrac{10}{30}+\dfrac{5}{95}\)

\(\Rightarrow\left(1+1+\dfrac{1}{43}+\dfrac{1}{8}\right)x=162+\dfrac{1}{3}+\dfrac{1}{19}\)

\(\Rightarrow\left(\dfrac{2.43.8}{43.8}+\dfrac{1.8}{43.8}+\dfrac{1.43}{43.8}\right)x=\dfrac{162.3.19}{3.19}+\dfrac{1.19}{3.19}+\dfrac{1.3}{19.3}\)

\(\Rightarrow\left(\dfrac{688}{344}+\dfrac{8}{344}+\dfrac{43}{344}\right)x=\dfrac{9234}{57}+\dfrac{19}{57}+\dfrac{3}{57}\)

\(\Rightarrow\dfrac{739}{344}x=\dfrac{9256}{57}\)

\(\Rightarrow x=\dfrac{9256}{57}:\dfrac{739}{344}=\dfrac{9256}{57}.\dfrac{344}{739}=\dfrac{\text{3184064}}{\text{42123}}\)

ta co(  x-10 / 30 )   -3  + ( x -14  / 43  ) -2  + ( x-5 / 95 ) -1 + ( x- 148  / 8) + 6 =0

=> (x- 10 -90 / 30  ) + ( x- 14-86  / 43 ) + ( x- 5- 95   /  95)  + ( x- 148 +48 ) =0

=> x-100 /30  +  x-100 / 43  + x- 100 / 95 +   x- 100 /  8 = 0

=> x-100 .( 1/30 + 1/43 +1/ 95 +1/ 8) =0

ma  1/30 + 1/43 + 1/ 95 + 1/8 khac 0 => x-100 =0 => x=100

h cho minh truoc da