Приведение дробей к наименьшему общему знаменателю

a) $$rac{7x}{12y}$$ и $$rac{5y}{8x}$$.

НОЗ = 24xy.

$$rac{7x}{12y} = rac{7x cdot 2x}{12y cdot 2x} = rac{14x^2}{24xy}$$.

$$rac{5y}{8x} = rac{5y cdot 3y}{8x cdot 3y} = rac{15y^2}{24xy}$$.

б) $$rac{3b}{a}$$ и $$rac{a}{a+b}$$.

НОЗ = a(a+b).

$$rac{3b}{a} = rac{3b(a+b)}{a(a+b)} = rac{3ab+3b^2}{a(a+b)}$$.

$$rac{a}{a+b} = rac{a cdot a}{a(a+b)} = rac{a^2}{a(a+b)}$$.

в) $$rac{m}{m+n}$$ и $$rac{n}{m-n}$$.

НОЗ = (m+n)(m-n).

$$rac{m}{m+n} = rac{m(m-n)}{(m+n)(m-n)} = rac{m^2-mn}{(m+n)(m-n)}$$.

$$rac{n}{m-n} = rac{n(m+n)}{(m-n)(m+n)} = rac{mn+n^2}{(m-n)(m+n)}$$.

г) $$rac{2a}{3a-3}$$ и $$rac{a+2}{a^2-1}$$.

$$rac{2a}{3a-3} = rac{2a}{3(a-1)}$$.

$$rac{a+2}{a^2-1} = rac{a+2}{(a-1)(a+1)}$$.

НОЗ = 3(a-1)(a+1).

$$rac{2a}{3(a-1)} = rac{2a(a+1)}{3(a-1)(a+1)} = rac{2a^2+2a}{3(a-1)(a+1)}$$.

$$rac{a+2}{(a-1)(a+1)} = rac{3(a+2)}{3(a-1)(a+1)} = rac{3a+6}{3(a-1)(a+1)}$$.