Question

Tìm x:

\(\dfrac{3}{\left(x+2\right)\left(x+5\right)}\)\(+\dfrac{5}{\left(x+5\right)\left(x+10\right)}\)\(+\dfrac{7}{\left(x+10\right)\left(x+17\right)}\)\(=\dfrac{x}{\left(x+2\right)\left(x+17\right)}\)

Answer 1

\(\dfrac{1}{x+2}-\dfrac{1}{x+5}+\dfrac{1}{x+5}-\dfrac{1}{x+10}+\dfrac{1}{x+10}-\dfrac{1}{x+17}\)\(=\dfrac{x}{15}\cdot\dfrac{15}{\left(x+2\right)\left(x+17\right)}\) \(\dfrac{1}{x+2}-\dfrac{1}{x+17}\)\(=\dfrac{x}{15}\cdot\left(\dfrac{1}{x+2}-\dfrac{1}{x+17}\right)\)

\(\dfrac{x}{15}=\left(\dfrac{1}{x+2}-\dfrac{1}{x+17}\right):\left(\dfrac{1}{x+2}-\dfrac{1}{x+17}\right)\)

\(\dfrac{x}{15}=1\)

\(x=15\cdot1\)

\(x=15\)

Answer 2

Đề HSG mà