Question

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

Answer 1

Answer:

solutions

Step-by-step explanation:

STEP1:Equation at the end of step 1 ((((m3)-(8•(m2)))+64m)-512) ——————————————————————————— ÷ ((((m3)+23m2)-64m)-512) ÷ (m2-5m-24) (((m2)+9m)+18) STEP 2 :Equation at the end of step2: ((((m3)-23m2)+64m)-512) ——————————————————————— ÷ (m3+8m2-64m-512) ÷ (m2-5m-24) (m2+9m+18) STEP3: m3 - 8m2 + 64m - 512 Simplify ———————————————————— m2 + 9m + 18 Checking for a perfect cube :

 3.1    m3 - 8m2 + 64m - 512  is not a perfect cube

Trying to factor by pulling out :

Answer 2

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

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

To Find : Simplify

Solution

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

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)

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

= m-8

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

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