Question

The quotient of 5n^2(m^2+2m-3)/10n(m^2-3m+2) divided by n^2(m^2-3m-18)/4n^2(m^2-8m+12)

Answer 1

$\dfrac{ 5n^2(m^2+2m-3)}{10n(m^2-3m+2)} \div \dfrac{n^2(m^2-3m-18)}{4n^2(m^2-8m+12)}$

$\dfrac{ 5n^2 (m + 3)(m - 1)}{10n( (m - 1)(m - 2)} \div \dfrac{n^2(m + 3)(m - 6)}{4n^2(m - 2)(m - 6)}$

$\dfrac{ 5n^2 (m + 3)(m - 1)}{10n( (m - 1)(m - 2)} \times \dfrac{4n^2(m - 2)(m - 6)}{n^2(m + 3)(m - 6)}$

$= 2n$