Question

помогите решить 1,3,5​

Answer 1

1.

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

2.

$\frac{x + 5}{x - 5} - \frac{x - 1}{x + 5} = \frac{(x + 5)(x + 5)}{(x - 5)(x + 5)} - \frac{(x - 1)(x - 5)}{ (x + 5)(x - 5)} = \\ \\ \frac{ {x}^{2} + 10x + 25 - {x}^{2} + 6x - 5 }{x^{2} - 25} = \frac{16x + 20}{ {x}^{2} - 25}$

3.

$\frac{3p}{3p + 2q} - \frac{ {9p}^{2} }{ {9p}^{2} + 12pq + {4q}^{2} } = \frac{3p}{3p + 2q} - \frac{ {9p}^{2} }{ {(3p + 2q})^{2} } = \\ \\ \frac{3p(3p + 2q) - {9p}^{2} }{ {(3p + 2q)}^{2} } = \frac{ {9p}^{2} + 6pq - 9p^{2} }{ {(3p + 2q)}^{2} } = \frac{6pq}{ {(3p + 2q)}^{2} }$