Question

Пожалуйста помогите как можно быстрее

Answer 1

Ответ:

1)

$\frac{8}{a}$

2)

$\frac{4a + b + b {}^{2} }{7a}$

3)

$\frac{4y}{4 - y {}^{2} } - \frac{y + 2}{y - 2}$

4)

$\frac{a + 1}{2}$

5)

$\frac{x + 4}{x - 4} - \frac{6x}{(x - 4) {}^{2} }$

6)

$\frac{x - x {}^{2} }{56x - 28x {}^{2} - 28 }$

7)

$\frac{30x - 1}{36x {}^{2} - 1 }$

Объяснение:

1)

$\frac{2a + 5b}{ab} - \frac{2a - 3b}{ab} = \\ = \frac{(2a + 5b) - (2a - 3b)}{ab} = \\ = \frac{2a + 5b - 2a + 3b}{ab} = \\ = \frac{8b}{ab} = \frac{8}{a}$

2)

$\frac{a + b}{7a} + \frac{3a + b {}^{2} }{7a} = \\ = \frac{a + b + 3a + b {}^{2} }{7a} = \\ = \frac{4a + b + b {}^{2} }{7a}$

3)

$\frac{y {}^{2} + 8y}{4 - y {}^{2} } - \frac{4y - 4}{4 - y {}^{2} } = \\ = \frac{y {}^{2} + 8y - (4y - 4)}{4 - y {}^{2} } = \\ = \frac{y {}^{2} + 8y - 4y + 4 }{4 - y {}^{2} } = \\ = \frac{y {}^{2} + 4y + 4 }{4 - y {}^{2} } = \\ = \frac{4y}{4 - y {}^{2} } + \frac{y {}^{2} + 4}{4 - y {}^{2} } = \\ = \frac{4y}{4 - y {}^{2} } - \frac{y {}^{2} + 4}{ y { }^{2} - 4} = \\ = \frac{4y}{4 - y {}^{2} } - \frac{(y + 2)(y + 2)}{(y - 2)(y + 2)} = \\ = \frac{4y}{4 - y {}^{2} } - \frac{y + 2}{y - 2}$

4)

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

5)

$\frac{16 - 7x}{(x - 4) {}^{2} } - \frac{x - x {}^{2} }{(4 - x) {}^{2} } = \\ = \frac{16 - 7x}{(x - 4) {}^{2} } + \frac{x - x {}^{2} }{(x - 4) {}^{2} } = \\ = \frac{16 - 7x + x - x {}^{2} }{(x - 4) {}^{2} } = \\ = \frac{16 - 6x - x {}^{2} }{(x - 4) {}^{2} } = \\ = \frac{16 - x {}^{2} - 6x }{(x - 4) {}^{2} } = \\ = \frac{16 - x {}^{2} }{(x - 4) {}^{2} } - \frac{6x }{(x - 4) {}^{2} } = \\ = - \frac{x {}^{2} - 16 }{(x - 4) {}^{2} } - \frac{6x}{(x - 4) {}^{2} } = \\ = - \frac{(x - 4)(x + 4)}{(x - 4) {}^{2} } - \frac{6x}{(x - 4) {}^{2} } = \\ = \frac{x + 4}{x - 4} - \frac{6x}{(x - 4) {}^{2} }$

6)

$\frac{3x}{4x - 4} + \frac{5x}{7 - 7x} = \\ = \frac{3x(7 - 7x) + 5x(4x - 4)}{(4x - 4)(7 - 7x)} = \\ = \frac{21x - 21x {}^{2} + 20x {}^{2} - 20x }{28x - 28x {}^{2} - 28 + 28x } = \\ = \frac{x - x {}^{2} }{56x - 28x {}^{2} - 28 }$

7)

$- \frac{5}{6x - 1} - \frac{6}{36x {}^{2} - 1 } = \\ = - \frac{5(6x + 1)}{(6x - 1)(6x + 1)} - \frac{6}{36x {}^{2} - 1 } = \\ = \frac{5(6x + 1) - 6}{36x {}^{2} - 1} = \\ = \frac{30x + 5 - 6}{36x {}^{2} - 1 } = \\ = \frac{30x - 1}{36x {}^{2} - 1}$