Question

Помогите ,люди добрые!

Answer 1

1) m/(1 - m²) + 1/(1 + m) = m/(1 - m²) + (1 - m)1/(1 - m²) =
 = (m + 1 - m)/(1 - m²) = 1/(1 - m²)

2) 2m/(m - 4) - (5m - 2)/(m² - 16) = 2m·(m + 4)/(m² - 16) - (5m - 2)/(m² - 16) =
= (2m² + 8m - 5m + 2)/(m² - 16) = (2m² + 3m + 2)/(m² - 16)

3) (1 - a)/3b² · b/(1 - a²) = (1 - a)·b/(3b² · (1 - a)(1 + a) = 1/(3b·(1 + a)

4) 5a/(a² - b²) - 15a²/(a - b) =  5a/(a² - b²) - 15a²·(a + b)/(a² - b²) =
= (5a - 15a³ - 15a²b)/(a² - b²) = 5a(1 - 3a² - 3ab)/(a² - b²)

5) (a² - b²)/(a - 3b) · (2a - b)/(a + b)² = (a - b)(a + b)/(a - 3b) · (2a - b)/(a + b)(a + b) =
= (a - b)(a + b)(2a - b)/[(a - 3b)(a + b)(a + b)] = (a - b)(2a - b)/[(a - 3b)(a + b)]  =
=(2a² - 2ab - ab +b²)/(a² - 3ab + ab -3b²) = (2a² - 3ab +b²)/(a² - 2ab - 3b²)

6) (a² - 49)/a² + 2ab + b²) : (a - 7)/(a + b) =
= (a - 7)(a + 7)(a + b)/[(a + b)(a + b)(a - 7)] =
=(а + 7)/(a + b)