Question

Сделайте пж нам два поставят дадим 10 баллов

Answer 1

1)

а)

$\frac{15a}{25b} = \frac{3a}{5b}$

б)

$\frac{15a + 15c}{25b} = \frac{15(a + c)}{25b} = \frac{3(a + c)}{5b} = \frac{3a + 3c}{5b}$

в)

$\frac{5a \times 5b}{10c} = \frac{25ab}{10c} = \frac{5ab}{2c}$

г)

$\frac{5a - 5b}{10c} = \frac{5(a - b)}{10c} = \frac{a - b}{2c}$

д)

$\frac{ {a}^{5} \times {a}^{3} }{ {a}^{10} } = \frac{ {a}^{8} }{ {a}^{10} } = \frac{1}{ {a}^{2} }$

е)

$\frac{ {a}^{5} + {a}^{3} }{ {a}^{10} } = \frac{ {a}^{3}( {a}^{2} + 1)}{ {a}^{10} } = \frac{ {a}^{2} + 1}{ {a}^{7} }$

ж)

$\frac{ {a}^{5} + {a}^{3} }{ {a}^{6} + {a}^{4} } = \frac{ {a}^{3} ( {a}^{2} + 1)}{ {a}^{4} ( {a}^{2} + 1)} = \frac{1}{a}$

2)

а)

$\frac{12 {a}^{3} {b}^{2} }{18 {a}^{4} } = \frac{2 {b}^{2} }{3a}$

б)

$\frac{12 {a}^{3} {b}^{2} + 6 {a}^{2} }{18 {a}^{4} } = \frac{6 {a}^{2}(2a {b}^{2} + 1)}{18 {a}^{4} } = \frac{2a {b}^{2} + 1 }{3 {a}^{2} }$

в)

$\frac{12 {a}^{3} {b}^{2} + 6 {a}^{2} }{18 {a}^{4} - 3 {a}^{2} } = \frac{6 {a}^{2} (2a {b}^{2} + 1)}{3 {a}^{2}(6 {a}^{2} - 1) } = \frac{2(2a {b}^{2} + 1)}{6 {a}^{2} - 1 } = \frac{4a {b}^{2} + 1}{6 {a}^{2} - 1}$

г)

$\frac{ {a}^{2} + ab }{a} = \frac{a(a + b)}{a} = a + b$

д)

$\frac{ {a}^{2} - ab }{b - a} = \frac{a(a - b)}{ - (a - b)} = - a$

е)

$\frac{ - {a}^{2} + ab}{ {a}^{2} b - a {b}^{2} } = \frac{ - a(a - b)}{ab(a - b)} = - \frac{1}{b}$

3)

а)

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

б)

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

в)

$\frac{2y + x}{ {x}^{2} - 4 {y}^{2} } = \frac{2y + x}{(x - 2y)(x + 2y)} = \frac{1}{x - 2y}$

г)

$\frac{2y - x}{ {x}^{2} - 4 {y}^{2} } = - \frac{x - 2y}{(x - 2y)(x + 2y)} = - \frac{1}{x + 2y}$

$[/tex]</p><p>4)</p><p>а)</p><p>[tex] \frac{ {m}^{2} - 25 }{ {m}^{2} + 10m + 25} = \frac{(m + 5)(m - 5)}{ {(m + 5)}^{2} } = \frac{m - 5}{m + 5}$

б)

$\frac{ {m}^{2} + 10m + 25 }{25 - {m}^{2} } = \frac{ {(m + 5)}^{2} }{(5 - m)(5 + m)} = \frac{m + 5}{5 - m}$

в)

$\frac{ {m}^{2} - 10m + 25}{ {m}^{2} - 25 } = \frac{ {(m - 5)}^{2} }{(m - 5)(m + 5)} = \frac{m - 5}{m + 5}$

г)

$\frac{25 - {m}^{2} }{ {m}^{2} - 10m + 25} = \frac{ - (m - 5)(5 + m)}{ {(m - 5)}^{2} } = - \frac{5 + m}{m - 5}$