Question

Решите всё то что есть на картинке

Answer 1

a)

$\frac{15 {x}^{2} }{6x + 15 {x}^{2} } = \frac{15 {x}^{2} }{3x(2 + 5x)} = \frac{5x}{2 + 5}$

б)

$\frac{9x + 9y}{36 {x}^{2} - 36 {y}^{2} } = \frac{9(x + y)}{36(x - y)(x + y)} = \frac{1}{4x - 4y}$

2. 1)

$\frac{5}{12a - 12b} - \frac{3}{16a - 16b} = \frac{5}{12(a - b)} - \frac{3}{16(a - b)} = \frac{20 - 9}{48(a - b)} = \frac{11}{48(a - b)}$

2)

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

3.

$\frac{3x - 9 {x}^{2} }{ {x}^{2} + 6x + 9 } \div \frac{1 - 9 {x}^{2} }{ {x}^{2} - 9 } = \frac{3x(1 - 3x)}{ {x + 3}^{2} } \times \frac{(x - 3)(x + 3)}{(1 - 3x)(1 + 3x)} = \frac{3x(x - 3)}{(x + 3)(1 + 3x)}$

х=1

$\frac{3(1 - 3)}{(1 + 3)(1 + 3)} = \frac{3( - 2)}{ {4}^{2} } = - \frac{6}{16} = - \frac{3}{8}$

4.

$\frac{z}{t} \times \frac{t}{k} = \frac{z}{k} \\ \frac{z}{k} = 5 \times 12 = 60$