Question

нужно решить самостоятельную работу.

Answer 1

1.

а)

$\frac{3x}{xy - 1} - \frac{2x}{xy - 1} = \frac{x}{xy - 1} \\$

2.

а)

$\frac{4 {x}^{2} - 9 }{2x + 3} = \frac{(2x - 3)(2x + 3)}{2x + 3} = 2x - 3 \\$

б)

$\frac{b - a}{5} \div \frac{a}{5} - \frac{ab + {b}^{2} }{ab} = \\ = \frac{b - a}{5} \times \frac{5}{a} - \frac{b(a + b)}{ab} = \\ = \frac{b - a}{a} - \frac{a + b}{a} = \\ = \frac{b - a - a - b}{a} = - \frac{2a}{a} = - 2$

с)

$\frac{ \sqrt[3]{189} }{ \sqrt[3]{56} \times \sqrt[4]{81} } = \sqrt[3]{ \frac{189}{56} } \times \frac{1}{ \sqrt[4]{ {3}^{4} } } = \\ = \sqrt[3]{ \frac{27}{8} } \times \frac{1}{3} = \frac{3}{2} \times \frac{1}{3} = \frac{1}{2} = 0.5$

3.

а)

$\sqrt{ {(15 \frac{5}{8}) }^{ \frac{2}{3} } - {(3 \frac{3}{8}) }^{ \frac{2}{3} } } = \sqrt{ {( \frac{125}{8}) }^{ \frac{2}{3} } - {( \frac{27}{8} )}^{ \frac{2}{3} } } = \\ = \sqrt{ {( \frac{5}{2} )}^{2} - {( \frac{3}{2}) }^{2} } = \sqrt{ \frac{25}{4} - \frac{9}{4} } = \\ = \sqrt{ \frac{16}{4} } = \sqrt{4} = 2$

б)

$log_{2}(16) + log_{2}(2) = log_{2}(16 \times 2) = \\ = log_{2}(32) = 5$

с)

$log_{2}(7) - log_{2}(63) + log_{2}(36) = log_{2}( \frac{7 \times 36}{63} ) = \\ = log_{2}( \frac{4}{1} ) = 2$

d)

$\sqrt[3]{48 + \sqrt{254 + \sqrt[5] {32} } } = \sqrt[3]{48 + \sqrt{254 + 2} } = \\ = \sqrt[3]{48 + \sqrt{256} } = \sqrt[3]{48 +16 } = \sqrt[3]{64} = \sqrt[3]{ {4}^{3} } = 4$

е)

$( \sqrt{14} - \sqrt{5} )( \sqrt{14} + \sqrt{5} ) = {( \sqrt{14} )}^{2} - {( \sqrt{5} }^{2} ) = \\ = 14 - 5 = 9$

f)

${8}^{4 log_{8}(3) } = {8}^{ log_{8}( {3}^{4} ) } = {8}^{ log_{8}(81) } = 81 \\$