Выполните действия: a)24a⁴/ b³ * b⁴/8a⁴ б)7xy²/ 2 : 14x²y² в)m+2n/m-n * m²-n²/5m+10n г)x²-2x+1/x²-25 : x-1/x²+5x

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вопрос

a) (24a⁴/b³) (b⁴/8a⁴)
= (24a⁴ b⁴) / (b³ * 8a⁴)
= 24a⁴b / 8a³b³
= 3a

b) (7xy²/2) / 14x²y²
= (7xy²/2) (1/14x²y²)
= (7xy²/2) (1/14xy²)
= 7/(2 * 14)
= 7/28
= 1/4

c) (m+2n/m-n) (m²-n²/5m+10n)
= [(m+2n)/(m-n)] [(m+n)(m-n)/(5(m+2n)]
= [(m+2n)/(m-n)] * [(m²-n²)/(5(m+2n)]
= [(m+2n)(m+n)/(m-n)(5(m+2n))]
= (m+n)/(5(m-n))
= (m+n)/(5m-5n)

d) (x²-2x+1)/(x²-25) : (x-1)/(x²+5x)
= [(x-1)(x-1)/(x-5)(x+5)] [(x²+5x)/(x-1)]
= [(x-1)(x-1)/(x-5)(x+5)] [x(x+5)/(x-1)]
= [(x-1)/(x-5)] * [x/(x+5)]
= (x(x-1))/(x+5)(x-5)