Đáp án:
$\text{ x = - 95 }$
Giải thích các bước giải:
$\dfrac{x+1}{94}+$ $\dfrac{x+2}{93}+$ $\dfrac{x+3}{92}+$ $\dfrac{x+4}{91}+$ $\dfrac{x+5}{90}+$ $\dfrac{x+6}{89}$
$⇔(\dfrac{x+1}{94}+1)+$ $(\dfrac{x+2}{93}+1)+$ $\dfrac{x+3}{92}+1)$
$=(\dfrac{x+4}{91}+1)+($ $\dfrac{x+5}{90}+1)+($ $\dfrac{x+6}{89}+1)$
$⇔\dfrac{x+95}{94}+$ $\dfrac{x+95}{93}+$ $\dfrac{x+95}{92}$
$=\dfrac{x+95}{91}+$ $\dfrac{x+95}{90}+$ $\dfrac{x+95}{89}$
$⇔\dfrac{x+95}{94}+$ $\dfrac{x+95}{93}+$ $\dfrac{x+95}{92}$ $-\dfrac{x+95}{91}-$ $\dfrac{x+95}{90}-$ $\dfrac{x+95}{89}$
$⇔(x+95).(\dfrac{1}{94}+$ $\dfrac{1}{93}+$ $\dfrac{1}{92}-$ $\dfrac{1}{91}-$ $\dfrac{1}{90}-$ $\dfrac{1}{89})=0$
$do:(x+95).(\dfrac{1}{94}+$ $\dfrac{1}{93}+$ $\dfrac{1}{92}-$ $\dfrac{1}{91}-$ $\dfrac{1}{90}-$ $\dfrac{1}{89})≠0$
$nên:(x+95).(\dfrac{1}{94}+$ $\dfrac{1}{93}+$ $\dfrac{1}{92}-$ $\dfrac{1}{91}-$ $\dfrac{1}{90}-$ $\dfrac{1}{89})=0$
$\text{⇔ x + 95 = 0 }$
$\text{⇔ x = 0 - 95 }$
$\text{⇔ x = - 95 }$
