3/(x+2)(x+5)+5/(x+5)(x+10)+7/(x+10)(x+17)=x/(x+2)(x+17) 26/09/2021 Bởi Ayla 3/(x+2)(x+5)+5/(x+5)(x+10)+7/(x+10)(x+17)=x/(x+2)(x+17)
Đáp án: \(x = 15\) Giải thích các bước giải: \[\begin{array}{l} \frac{3}{{\left( {x + 2} \right)\left( {x + 5} \right)}} + \frac{5}{{\left( {x + 5} \right)\left( {x + 10} \right)}} + \frac{7}{{\left( {x + 10} \right)\left( {x + 17} \right)}} = \frac{x}{{\left( {x + 2} \right)\left( {x + 17} \right)}}\\ DK:\,\,\,\left\{ \begin{array}{l} x \ne – 2\\ x \ne – 5\\ x \ne – 10\\ x \ne – 17 \end{array} \right.\\ pt \Leftrightarrow \frac{{x + 5 – \left( {x + 2} \right)}}{{\left( {x + 2} \right)\left( {x + 5} \right)}} + \frac{{x + 10 – \left( {x + 5} \right)}}{{\left( {x + 5} \right)\left( {x + 10} \right)}} + \frac{{x + 17 – \left( {x + 10} \right)}}{{\left( {x + 10} \right)\left( {x + 17} \right)}} = \frac{x}{{\left( {x + 2} \right)\left( {x + 17} \right)}}\\ \Leftrightarrow \frac{1}{{x + 2}} – \frac{1}{{x + 5}} + \frac{1}{{x + 5}} – \frac{1}{{x + 10}} + \frac{1}{{x + 10}} – \frac{1}{{x + 17}} = \frac{x}{{\left( {x + 2} \right)\left( {x + 17} \right)}}\\ \Leftrightarrow \frac{1}{{x + 2}} – \frac{1}{{x + 17}} = \frac{x}{{\left( {x + 2} \right)\left( {x + 17} \right)}}\\ \Leftrightarrow x + 17 – x – 2 = x\\ \Leftrightarrow x = 15\,\,\,\left( {tm} \right).\\ Vay\,\,\,x = 15. \end{array}\] Bình luận
Đáp án:
\(x = 15\)
Giải thích các bước giải:
\[\begin{array}{l}
\frac{3}{{\left( {x + 2} \right)\left( {x + 5} \right)}} + \frac{5}{{\left( {x + 5} \right)\left( {x + 10} \right)}} + \frac{7}{{\left( {x + 10} \right)\left( {x + 17} \right)}} = \frac{x}{{\left( {x + 2} \right)\left( {x + 17} \right)}}\\
DK:\,\,\,\left\{ \begin{array}{l}
x \ne – 2\\
x \ne – 5\\
x \ne – 10\\
x \ne – 17
\end{array} \right.\\
pt \Leftrightarrow \frac{{x + 5 – \left( {x + 2} \right)}}{{\left( {x + 2} \right)\left( {x + 5} \right)}} + \frac{{x + 10 – \left( {x + 5} \right)}}{{\left( {x + 5} \right)\left( {x + 10} \right)}} + \frac{{x + 17 – \left( {x + 10} \right)}}{{\left( {x + 10} \right)\left( {x + 17} \right)}} = \frac{x}{{\left( {x + 2} \right)\left( {x + 17} \right)}}\\
\Leftrightarrow \frac{1}{{x + 2}} – \frac{1}{{x + 5}} + \frac{1}{{x + 5}} – \frac{1}{{x + 10}} + \frac{1}{{x + 10}} – \frac{1}{{x + 17}} = \frac{x}{{\left( {x + 2} \right)\left( {x + 17} \right)}}\\
\Leftrightarrow \frac{1}{{x + 2}} – \frac{1}{{x + 17}} = \frac{x}{{\left( {x + 2} \right)\left( {x + 17} \right)}}\\
\Leftrightarrow x + 17 – x – 2 = x\\
\Leftrightarrow x = 15\,\,\,\left( {tm} \right).\\
Vay\,\,\,x = 15.
\end{array}\]
Đáp án:
Giải thích các bước giải: