Question

помогите решить дам 50 баллов​

Answer 1

1)

$\frac{ab - {b}^{2} }{8} \times \frac{32a}{ {b}^{3} } = \frac{(ab - {b}^{2} ) \times 32a}{8 \times {b}^{3} } = \frac{b \times (a - b) \times 4 \times 8 \times a}{8 \times {b}^{3} } = \frac{4a(a - b)}{ {b}^{2} } = \frac{4 {a}^{2} - 4ab}{ {b}^{2} }$

2)

$\frac{ {m}^{2} - mn}{ {m}^{2} + mn } \times \frac{ {m}^{2}n + m {n}^{2} }{ {m}^{3} - {m}^{2}n } = \frac{m(m - n)}{m(m + n)} \times \frac{mn(m + n)}{ {m}^{2}(m - n) } = \frac{m - n}{m + n} \times \frac{n(m + n)}{m(m - n)} = \frac{(m - n) \times n \times (m + n)}{(m + n) \times m \times (m - n)} = \frac{n}{m}$

3)

$\frac{ {x}^{2} - 16 }{ {x}^{3} - 3 {x}^{2} } \times \frac{ {x}^{2} - 9}{ {x}^{2} + 4x } = \frac{ {x}^{2} - {4}^{2} }{ {x}^{2} (x - 3)} \times \frac{ {x}^{2} - {3}^{2} }{x(x + 4)} = \frac{(x - 4)(x + 4)}{ {x}^{2} (x - 3)} \times \frac{(x - 3)(x + 3)}{x(x + 4)} = \frac{(x - 4) \times (x + 4) \times (x - 3) \times (x + 3)}{ {x}^{2} \times (x - 3) \times x \times (x + 4) } = \frac{(x - 4) \times (x + 3)}{ {x}^{2} \times x} = \frac{ {x}^{2} + 3x - 4x - 12 }{ {x}^{3} } = \frac{ {x}^{2} - x - 12}{ {x}^{3} }$

4)

$\frac{5 {y}^{2} - 20y + 20}{ {y}^{3} - 1} \times \frac{3 {y}^{2} + 3y + 3}{10y - 20} = \frac{5( {y}^{2} - 4y + 4) }{(y - 1)( {y}^{2} + y + 1) } \times \frac{3( {y}^{2} + y + 1)}{10(y - 2)} = \frac{5 {(y - 2)}^{2} }{(y - 1)( {y}^{2} + y + 1) } \times \frac{3 ( {y}^{2} + y + 1) }{10(y - 2)} = \frac{5 {(y - 2)}^{2} \times 3( {y}^{2} + y + 1)}{(y - 1)( {y}^{2} + y + 1) \times 10(y - 2)} = \frac{(y - 2) \times 3}{(y - 1) \times 2} = \frac{3y - 6}{2y - 2}$

1)

$\frac{x + 1}{3x} \div \frac{ {x}^{2} + 2x + 1 }{9 {x}^{2} } = \frac{x + 1}{3x} \times \frac{9 {x}^{2} }{ {x}^{2} + 2x + 1} = \frac{x + 1}{3x} \times \frac{ {(3x)}^{2} }{ {(x + 1)}^{2} } = \frac{(x + 1) \times 3x \times 3x}{3x \times (x + 1) \times (x + 1)} = \frac{3x}{x + 1}$

2)

$\frac{ {x}^{2} - 2x }{3x + 3} \div \frac{5x - 10}{x + 1} = \frac{ {x}^{2} - 2x}{3x + 3} \times \frac{x + 1}{5x - 10} = \frac{x(x - 2)}{3(x + 1)} \times \frac{x + 1}{5(x - 2)} = \frac{x \times (x - 2) \times (x + 1)}{3 \times (x + 1) \times 5 \times (x - 2)} = \frac{x}{3 \times 5} = \frac{x}{15}$

3)

$(n - 7) \div \frac{ {n}^{2} - 14n + 49}{ {n}^{2} - 49 } = (n - 7) \times \frac{ {n}^{2} - 49}{ {n}^{2} - 14n + 49} = \frac{(n - 7) \times ( {n}^{2} - {7}^{2} )}{ {(n - 7)}^{2} } = \frac{(n - 7) \times (n - 7)(n + 7)}{(n - 7)(n - 7)} = n + 7$

4)

$\frac{ {a}^{2} - 4 {b}^{2} }{9 {a}^{2} - {b}^{2} } \div \frac{ {a}^{2} + 4ab + 4 {b}^{2} }{9 {a}^{2} - 6ab + {b}^{2} } = \frac{ {a}^{2} - 4 {b}^{2} }{9 {a}^{2} - {b}^{2} } \times \frac{9 {a}^{2} - 6ab + {b}^{2} }{ {a}^{2} + 4ab + 4 {b}^{2} } = \frac{ {a}^{2} - {(2b)}^{2} }{ {(3a)}^{2} - {b}^{2} } \times \frac{ {(3a)}^{2} - 6ab + {b}^{2} }{ {a}^{2} + 4ab + {(2b)}^{2} } = \frac{(a - 2b)(a + 2b)}{(3a - b)(3a + b)} \times \frac{ {(3a - b)}^{2} }{ {(a + 2b)}^{2} } = \frac{(a - 2b)(a + 2b) \times (3a - b)(3a - b)}{(3a - b)(3a + b) \times (a + 2b)(a + 2b)} = \frac{(a - 2b) \times (3a - b)}{(3a + b) \times (a + 2b)} = \frac{3 {a}^{2} - ab - 6ab + 2 {b}^{2} }{3 {a}^{2} + 6ab + ab + 2 {b}^{2} } = \frac{3 {a}^{2} - 7ab + 2 {b}^{2} }{3 {a}^{2} + 7ab + 2 {b}^{2} }$