Question

#27, Упростите выражение 1) и 2).​

Answer 1

1)

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

2)

$\frac{x+7}{3x+12}-\frac{2}{x}+\frac{7x+40}{3x^2+12x}=\frac{x(x+7)-6(x+4)+7x+40}{3x(x+4)}=\\\\=\frac{(x+4)^2}{3x(x+4)}=\frac{x+4}{3x}$

Answer 2

$1) \: \frac{ {a}^{2} + {b}^{2} }{ {a}^{2} - {b}^{2} } - \frac{b}{a + b} + \frac{b}{b - a} \\ \frac{ {a}^{2} + {b}^{2} }{(a - b) \times (a + b)} - \frac{b}{a + b} + \frac{b}{ - (a - b)} \\ \frac{ {a}^{2} + {b}^{2} }{(a - b) \times (a + b)} - \frac{b}{a + b} - \frac{b}{a - b} \\ \frac{ {a}^{2} + {b}^{2} - b \times (a - b) - b \times (a + b)}{(a - b) \times (a + b)} \\ \frac{ {a}^{2} + {b}^{2 } - ab + {b}^{2} - ab - {b}^{2} }{(a - b) \times (a + b)} \\ \frac{ {a}^{2} - 2ab + {b}^{2} }{(a - b) \times (a + b)} \\ \frac{(a - b {)}^{2} }{(a - b) \times (a + b)} \\ \frac{a - b}{a + b}$

$2) \: \frac{x + 7}{3x + 12} - \frac{2}{x} + \frac{7x + 40}{3 {x}^{2} + 12x } \\ \frac{x + 7}{3(x + 4)} - \frac{2}{x} + \frac{7x + 40}{3x(x + 4)} \\ \frac{x \times (x + 7) - 6(x + 4) + 7x + 40}{3x(x + 4)} \\ \frac{ {x}^{2} + 7x - 6x - 24 + 7x + 40 }{3x(x + 4)} \\ \frac{ {x}^{2} + 8x + 16}{3x(x + 4)} \\ \frac{(x + 4 {)}^{2} }{3x(x + 4)} \\ \frac{x + 4}{3x}$