Question

Tính M = 3\(\dfrac{1}{437}\) * \(\dfrac{1}{762}\) - \(\dfrac{1}{139}\) * 4\(\dfrac{761}{762}\) - \(\dfrac{4}{417\cdot762}\) + \(\dfrac{5}{139}\) .

Giúp mình giải chi tiết bài này nha, các bạn.

Answer 1

Đặt 761=a; 139=b

\(M=\left(3+\dfrac{1}{3b}\right)\cdot\dfrac{1}{a+1}-\dfrac{1}{b}\cdot\left(4+\dfrac{a}{a+1}\right)-\dfrac{4}{\left(a+1\right)\cdot3b}+\dfrac{5}{b}\)

\(=\dfrac{9b+1}{3b}\cdot\dfrac{1}{a+1}-\dfrac{1}{b}\cdot\dfrac{4a+4}{a+1}-\dfrac{4}{3b\left(a+1\right)}+\dfrac{5}{b}\)

\(=\dfrac{9b+1-3\left(4a+4\right)-4+15\left(a+1\right)}{3b\left(a+1\right)}\)

\(=\dfrac{9b+1-12a-12-4+15a+15}{3b\left(a+1\right)}\)

\(=\dfrac{3a+9b}{3b\left(a+1\right)}=\dfrac{3\left(a+3b\right)}{3b\left(a+1\right)}=\dfrac{a+3b}{b\left(a+1\right)}\)

\(=\dfrac{761+3\cdot139}{139\left(761+1\right)}=\dfrac{589}{52959}\)