Question

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Answer 1

Ответ:

1.

Дробь имеет смысл, когда знаменатель не равен 0.

${x}^{2} - 16\ne0 \\ {x}^{2} \ne16 \\ x\ne\pm4$

2.

$\frac{14 {x}^{2} {b}^{4} }{21 {x}^{6} {b}^{3} } = \frac{2b}{3 {x}^{4} }$

3.

$5a + \frac{2b - 15a {}^{2} }{3a} = \frac{5a \times 3a + 2b - 15a {}^{2} }{3a} = \\ = \frac{15 {a}^{2} + 2b - 15a {}^{2} }{3a} = \frac{2b}{3a} \\ \\ a = 4 \\ b = - 12 \\ \\ \frac{2 \times ( - 12)}{3 \times 4} = - 2$

4.

а)

$\frac{b}{18a} + \frac{b}{24a} = \frac{b}{6 \times 3a} + \frac{b}{6 \times 4a} = \\ = \frac{4b + 3b}{72a} = \frac{7b}{72a}$

б)

$\frac{5x - 7}{ {x}^{2} - 4} - \frac{3x - 2}{2 - x} = \frac{5x - 7}{( x - 2)(x + 2)} + \frac{3x - 2}{x - 2} = \\ = \frac{5x - 7 + (3x - 2)(x + 2)}{(x - 2)(x + 2)} = \\ = \frac{5x - 7 + 3 {x}^{2} + 6x - 2x - 4 }{ {x}^{2} - 4 } = \\ = \frac{3 {x}^{2} + 9x - 11 }{ {x}^{2} - 4}$

5.

а)

$\frac{ {a}^{2} + 2ab + b {}^{2} }{ {x}^{5} } \times \frac{ {x}^{6} }{a {}^{2} - b {}^{2} } = \\ = \frac{x(a + b) {}^{2} }{(a - b)(a + b)} = \frac{x(a + b)}{a - b}$

б)

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

6.

а

$\frac{p - q}{p} \times ( \frac{p}{p - q} + \frac{p}{q} ) = \frac{p - q}{p} \times \frac{pq + p(p - q)}{q(p - q)} = \\ = \frac{pq + p {}^{2} - pq}{pq} = \frac{p {}^{2} }{pq} = \frac{p}{q}$

б

на фото