Question

выполните умножения и деления алгебраических дробей:
1)(а²-4ав+4в²/у⁶)/(×у⁷/а²-4в²​)
2)(4а²-1)/а²-9:(6а+3)/а+3
Срочно пж❤️

Answer 1

$\dfrac{a^2-4ab+4b^2}{y^6}\times\dfrac{y^7}{a^2-4b^2} = \dfrac{a^2-4ab+4b^2}{a^2-4b^2}\times\dfrac{y^7}{y^6} = \dfrac{(a-2b)^2}{(a-2b)(a+2b)}\times\dfrac{y^7}{y^6} = \dfrac{a-2b}{a+2b}\times y = \dfrac{(a-2b)\cdot y}{a+2b}$

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