Question

Помогите пожалуйста тема алгебраические дроби.

Answer 1

1.
$a) \frac{14 {a}^{4} b}{49{a}^{3} {b}^{2} } = \frac{2a}{7b}$
$b) \frac{3x}{ {x}^{2} + 4x } = \frac{3}{x + 4}$
$c) \frac{ {y}^{2} - {z}^{2} }{2y + 2z} = \frac{(y - z)(y + z)}{2(y + z)} = \frac{y - z}{2}$
2.
$a)\frac{3x - 1}{ {x}^{2} } + \frac{x - 9}{3x} = \frac{9x - 3 + {x}^{2} - 9x }{3 {x}^{2} } = \frac{ {x}^{2} - 3}{3 {x}^{2} }$
$b) \frac{1}{2a - b} - \frac{1}{2a + b} = \frac{2a + b - 2a + b}{4 {a}^{2} - {b}^{2} } = \frac{2 {b}^{2} }{4 {a}^{2} - {b}^{2} }$
$c) \frac{5}{c + 3} - \frac{5c - 2}{ {c}^{2} + 3c } = \frac{5c - 5c + 2}{c(c + 3)} = \frac{2}{ {c}^{2} + 3c }$
3.
$\frac{ {a}^{2} - b}{a}$
При а=0,2; б=-5

$\frac{ {0.2}^{2} - ( - 5)}{0.2} = \frac{0.04 + 5}{0.2} = \frac{5.04}{0.2} = 25.2$
4.
$\frac{3x}{x - 3} - \frac{x + 15}{ {x}^{2} - 9} - \frac{2}{x} = \frac{3 {x}^{2} (x + 3) - {x}^{2} - 15x - 2 {x}^{2} + 18 }{x( {x}^{2} - 9)} = \frac{ {x}^{3} + 9 {x}^{2} - {x}^{2} - 15 - 2 {x}^{2} + 18 }{x( {x}^{2} - 9) } = \frac{ {x}^{3} + 6 {x}^{2} + 3}{ {x}^{3} - 9x}$
5.
При любых, кроме а=0