Question

rút gọn biểu thức: C=2/k(2k)+2/(k+2)(k+4)+2/(k+4)(k+6)

 

 

Answer 1

\(C=\dfrac{2}{k\cdot2k}+\dfrac{2}{\left(k+2\right)\left(k+4\right)}+\dfrac{2}{\left(k+4\right)\left(k+6\right)}\\ =\dfrac{1}{k^2}+\left(\dfrac{1}{k+2}-\dfrac{1}{k+4}+\dfrac{1}{k+4}-\dfrac{1}{k+6}\right)\\ =\dfrac{1}{k^2}+\left(\dfrac{1}{k+2}-\dfrac{1}{k+6}\right)\\ =\dfrac{1}{k^2}+\dfrac{k+6-k-2}{\left(k+2\right)\left(k+6\right)}\\ =\dfrac{1}{k^2}+\dfrac{4}{\left(k+2\right)\left(k+6\right)}\\ =\dfrac{\left(k+2\right)\left(k+6\right)+4k^2}{k^2\left(k+2\right)\left(k+6\right)}\\ =\dfrac{5k^2+8k+12}{k^2\left(k+2\right)\left(k+6\right)}\)