[tex]a) \frac{4}{ \sqrt{7} } + \frac{1}{2 \sqrt{7} } - \frac{3}{5 \sqrt{7} } + \frac{9}{10 \sqrt{7} } = \frac{4 \sqrt{7} }{7} + \frac{ \sqrt{7} }{2 \times 7} - \frac{3 \sqrt{7} }{5 \times 7} + \frac{9 \sqrt{7} }{10 \times 7} = \frac{4 \sqrt{7} }{7} + \frac{ \sqrt{7} }{14} - \frac{3 \sqrt{7} }{35} + \frac{9 \sqrt{7} }{70} = \frac{10 \times 4 \sqrt{7} }{10 \times 7} + \frac{5 \sqrt{7} }{5 \times 14} - \frac{2 \times 3 \sqrt{7} }{2 \times 35} + \frac{9 \sqrt{7} }{70} = \frac{40 \sqrt{7} }{70} + \frac{5 \sqrt{7} }{70} - \frac{6 \sqrt{7} }{70} + \frac{9 \sqrt{7} }{70} = \frac{40 \sqrt{7} + 5 \sqrt{7} - 6 \sqrt{7} + 9 \sqrt{7} }{70} = \frac{(40 + 5 - 6 + 9) \sqrt{7} }{70} = \frac{48 \sqrt{7} }{70} ^{(2} = \frac{24 \sqrt{7} }{35} [/tex]
