Question

Виконай дії:
1) (2p ^ 2)/(25c ^ 2) * (5c)/(6p ^ 2)
2)(a ^ 2 - 2ab + b ^ 2)/(cd) * (d ^ 2)/(ba - b ^ 2) 3) 3m ^ 2)/(7p) ^ 3 :(- 9m^ 3 35p )
4) (n ^ 2 - 9)/(3n - 12) / (2n + 6)/(5n - 20)​

Answer 1

Завдання: Виконай дії

1) $\dfrac{2 {p}^{2} }{25 {c}^{2} } \cdot \dfrac{5c}{6 {p}^{2} }$

2) $\dfrac{ {a}^{2} - 2ab + {b}^{2} }{cd} \cdot \dfrac{ {d}^{2} }{ba - {b}^{2} }$

3) $\dfrac{3 {m}^{2} }{7p} : ( - \dfrac{9 {m}^{3} }{35p})$

4) $\dfrac{ {n}^{2} - 9}{3n - 12} :\dfrac{2n + 6}{5n - 20}$

Розв'язання:

$1) \quad \dfrac{2 {p}^{2} }{25 {c}^{2} } \cdot \dfrac{5c}{6 {p}^{2} } = \dfrac{1}{5c \cdot \: 3} = \dfrac{1}{15c}$

$2)\quad \dfrac{ {a}^{2} - 2ab + {b}^{2} }{cd} \cdot \dfrac{ {d}^{2} }{ba - {b}^{2} }=\dfrac{ {(a-b)}^{2} }{cd} \cdot \dfrac{ {d}^{2} }{b(a - b) }=\dfrac{ a-b }{c} \cdot \dfrac{ d }{b }=\dfrac{ d(a-b)}{bc}$

$3) \quad \dfrac{3 {m}^{2} }{7p} : ( - \dfrac{9 {m}^{3} }{35p}) = \dfrac{3 {m}^{2} }{7p} \cdot ( - \dfrac{35p }{9 {m}^{3} }) = \dfrac{1}{1} \cdot( - \dfrac{5}{3m} ) = - \dfrac{5}{3m}$

$4) \quad \dfrac{ {n}^{2} - 9}{3n - 12} :\dfrac{2n + 6}{5n - 20} = \dfrac{ {n}^{2} - 9}{3n - 12} \cdot\dfrac{5n - 20}{2n + 6} =\\ \\ =\dfrac{ (n - 3)(n + 3)}{3(n - 4)} \cdot\dfrac{5(n - 4)}{2(n + 3)} = \dfrac{ n - 3}{3} \cdot\dfrac{5}{2} = \dfrac{5(n - 3)}{6}$

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