Tính hợp lí a) 3/5.7 + 3/7.9 +...+ 3/59.61 b) 5/22 + 3/13 -1/2 / 4/13 -2/11 +3/2

* Hướng dẫn giải

a)

$\begin{array}{l}\frac{3}{5.7}+\frac{3}{7.9}+\mathrm{...}+\frac{3}{59.61}\\ =\frac{3}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+\mathrm{...}+\frac{2}{59.61}\right)\\ =\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\mathrm{...}+\frac{1}{59}-\frac{1}{61}\right)\\ =\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{61}\right)=\frac{3}{2}.\frac{56}{305}=\frac{844}{305}\end{array}$

b)

$$\begin{gathered} \frac{\frac{5}{22}+\frac{3}{13}-\frac{1}{2}}{\frac{4}{13}-\frac{2}{11}+\frac{3}{2}}=\frac{\left(\frac{5}{22}+\frac{3}{13}-\frac{1}{2}\right).\left(\mathrm{2.11.13}\right)}{\left(\frac{4}{13}-\frac{2}{11}+\frac{3}{2}\right).\left(\mathrm{2.11.13}\right)} \\ =\frac{65+66-143}{88-52+429}=\frac{-12}{465}=\frac{-4}{155} \end{gathered}$$