Question

СРОЧНО!1.Приведите дроби к общему знаменателю a-b/5a+5b и a²/a²-b²,x+y/6x-6y и y/x²-y²,13c/12c-12d и 17d/d²-c²,26z²/45t-45z и 3t/z²-t²​

Answer 1

Ответ:

1.

$\frac{ a- b}{5a + 5b} = \frac{a -b }{5(a + b)} \\ \frac{ {a}^{2} }{a {}^{2} - b {}^{2} } = \frac{ {a}^{2} }{(a - b)(a + b)}$

общий знаменатель:

$5(a - b)(a +b )$

приводим:

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

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

2.

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

общий знаменатель:

$6(x - y)(x + y)$

приводим:

$\frac{x + y}{6(x - y)} \times \frac{x + y}{x + y} = \frac{ {(x + y)}^{2} }{6(x - y)(x + y)} = \\ = \frac{ {x}^{2} + 2xy + {y}^{2} }{6( {x}^{2} - {y}^{2} )}$

$\frac{y}{(x - y)(x + y)} \times \frac{6}{6} = \frac{6y}{6( {x}^{2} - {y}^{2}) }$

3.

$\frac{13c}{12c - 12d} = \frac{13c}{12(c - d)} \\ \frac{17d}{d {}^{2} - c {}^{2} } = - \frac{17d}{ {c}^{2} - d {}^{2} } = \frac{ - 17d}{(c - d)(c + d)}$

общий знаменатель:

$12(c - d)( c+ d)$

приводим:

$\frac{13c}{12(c - d)} \times \frac{c + d}{ c+ d} = \frac{13 {c}^{2} + 13cd}{12( {c}^{2} - d {}^{2}) }$

$\frac{ - 17d}{(c - d)(c + d)} \times \frac{12}{12} = \frac{ - 204d}{12( {c}^{2} - d {}^{2}) }$

4.

$\frac{26 {z}^{2} }{45t - 45z} = \frac{26 {z}^{2} }{45(t - z)} \\ \frac{3t}{ {}^{} z {}^{2} - t {}^{2} } = - \frac{3t}{t {}^{2} - z {}^{2} } = \frac{ - 3t}{(t - z)(t + z)}$

общий знаменатель:

$45(t - z)(t + z)$

приводим:

$\frac{26 {z}^{2} }{45(t - z)} \times \frac{t + z}{t + z} = \frac{26 {z}^{2}t + 26z {}^{3} }{45( {t}^{2} - z {}^{2} ) }$

$\frac{ - 3t}{(t - z)(t + z)} \times \frac{45}{45} = - \frac{135}{45( {t}^{2} - z {}^{2} ) }$