Question

Simplify : m2 – 5m - 24 / ( m + 3 ) ( m + 8 ) x m2 - 64 / ( m – 8)2​

Answer 1

Given :  { (m² - 5m - 24 )/(m + 3)(m + 8)  } × {(m² - 64)/(m - 8)²}

$\dfrac{m^2-5m-24}{(m+3)(m+8)} \times \dfrac{m^2-64}{(m-8)^2}$

To Find : Simplify

Solution

$\dfrac{m^2-5m-24}{(m+3)(m+8)} \times \dfrac{m^2-64}{(m-8)^2}$

m² - 5m - 24

Using middle term split

= m² - 8m + 3m - 24

= m( m - 8) + 3(m - 8)

= (m -8)(m + 3)

m² - 64

= m² - 8²

using identity a² - b² = (a + b)(a - b)

= (m + 8) (m - 8)

$=\dfrac{(m+3)(m-8)}{(m+3)(m+8)} \times \dfrac{(m+8)(m-8)}{(m-8)^2}$

= 1

$\dfrac{m^2-5m-24}{(m+3)(m+8)} \times \dfrac{m^2-64}{(m-8)^2}=1$

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