3/(x+2)(x+5)+5/(x+5)(x+10)+7/(x+10)(x+17)=x/(x+2)(x+17)

Đáp án:

Giải thích các bước giải:

Đáp án:

$x = 15$

Giải thích các bước giải: $\begin{array}{l} \frac{3}{{\left( {x + 2} \right)\left( {x + 5} \right)}} + \frac{5}{{\left( {x + 5} \right)\left( {x + 10} \right)}} + \frac{7}{{\left( {x + 10} \right)\left( {x + 17} \right)}} = \frac{x}{{\left( {x + 2} \right)\left( {x + 17} \right)}}\\ DK:\,\,\,\left\{ \begin{array}{l} x \ne - 2\\ x \ne - 5\\ x \ne - 10\\ x \ne - 17 \end{array} \right.\\ pt \Leftrightarrow \frac{{x + 5 - \left( {x + 2} \right)}}{{\left( {x + 2} \right)\left( {x + 5} \right)}} + \frac{{x + 10 - \left( {x + 5} \right)}}{{\left( {x + 5} \right)\left( {x + 10} \right)}} + \frac{{x + 17 - \left( {x + 10} \right)}}{{\left( {x + 10} \right)\left( {x + 17} \right)}} = \frac{x}{{\left( {x + 2} \right)\left( {x + 17} \right)}}\\ \Leftrightarrow \frac{1}{{x + 2}} - \frac{1}{{x + 5}} + \frac{1}{{x + 5}} - \frac{1}{{x + 10}} + \frac{1}{{x + 10}} - \frac{1}{{x + 17}} = \frac{x}{{\left( {x + 2} \right)\left( {x + 17} \right)}}\\ \Leftrightarrow \frac{1}{{x + 2}} - \frac{1}{{x + 17}} = \frac{x}{{\left( {x + 2} \right)\left( {x + 17} \right)}}\\ \Leftrightarrow x + 17 - x - 2 = x\\ \Leftrightarrow x = 15\,\,\,\left( {tm} \right).\\ Vay\,\,\,x = 15. \end{array}$