Question

Алгебра 7 класс.
Помогите пожалуйста. СРОЧНО!

Answer 1

Задание №1

а) $\frac{22p^4q^2}{99p^5q} = \frac{2q}{9p}$

б) $\frac{7a}{a^2+5a} = \frac{7a}{a(a+5)} = \frac{7}{a+5}$

в) $\frac{x^2-y^2}{4x+4y} = \frac{(x-y)(x+y)}{4(x+y)} = \frac{x-y}{4}$

Задание №2

a) $\frac{y-20}{4y} + \frac{5y-2}{y^2} = \frac{y(y-20)+4(5y-2)}{4y^2} = \frac{y^2-20y+20y-8}{4y^2} = \frac{y^2-8}{4y^2}$

б) $\frac{1}{5c-2} - \frac{1}{5c+2} = \frac{5c + 2 - 5c + 2}{(5c-2)(5c+2)} = \frac{4}{(5c-2)(5c+2)}$

Задание №3

а) $\frac{42x^5}{y^4}\cdot \frac{y^2}{14x^5} = \frac{42x^5y^2}{14x^5y^4} = \frac{3}{y^2}$

б) $\frac{63a^3b}{c} : (18a^2b) = \frac{63a^3b}{18a^2bc} = \frac{7a}{2c}$

в) $\frac{4a^2-1}{a^2-9} : \frac{6a + 3}{a+3} = \frac{(2a-1)(2a+1)(a+3)}{3(a-3)(a+3)(2a+1)} =\frac{2a-1}{3a-9}$

г) $\frac{p-q}{p} \cdot (\frac{p}{p-q} + \frac{p}{q}) = (\frac{p-q}{p} \cdot \frac{p}{p-q}) + (\frac{p-q}{p} \cdot \frac{p}{q}) = 1 + \frac{p-q}{q} = 1+ \frac{p}{q} - 1 = \frac{p}{q}$

Задание №4

a)

$(\frac{x+y}{x-y} - \frac{x-y}{x+y}) : \frac{xy}{x^2 - y^2} = (\frac{(x+y)^2 - (x-y)^2}{x^2-y^2}) : \frac{xy}{x^2 - y^2} = \\\\ (\frac{x^2+2xy+y^2-x^2 +2xy-y^2}{x^2-y^2} ) : \frac{xy}{x^2 - y^2} = \frac{4xy(x^2-y^2)}{xy(x^2 - y^2)} = 4$

б)

$(\frac{a}{a-5} - \frac{a}{a+5} - \frac{a+25}{25-a^2}) \cdot \frac{a-5}{a^2+10a+25} = (\frac{a(a+5) - a(a-5) + a-25}{(a-5)(a+5)}) \cdot \frac{a-5}{(a+5)^2} = \\\\ \frac{(a^2+5a - a^2 + 5a + a-25)(a-5)}{(a-5)(a+5)(a+5)(a+5)} = \frac{11a-25}{(a+5)^3}$