a) (24a⁴/b³) (b⁴/8a⁴= (24a⁴ b⁴) / (b³ * 8a⁴= 24a⁴b / 8a³b= 3a
b) (7xy²/2) / 14x²y= (7xy²/2) (1/14x²y²= (7xy²/2) (1/14xy²= 7/(2 * 14= 7/2= 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)
a) (24a⁴/b³) (b⁴/8a⁴
= (24a⁴ b⁴) / (b³ * 8a⁴
= 24a⁴b / 8a³b
= 3a
b) (7xy²/2) / 14x²y
= (7xy²/2) (1/14x²y²
= (7xy²/2) (1/14xy²
= 7/(2 * 14
= 7/2
= 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)