Factor out the common term 200m^3
9/20m^3(m + 5) - 2m^2(3m^2 + 16m + 5
Split the second term in 3m^2 + 16m + 5 into these two terms
9/20m^3(m + 5) - 2m^2/3m^2 + 15m + m + 5
Factor out the common terms in the two terms, then in the last two terms;
9/20m^3(m + 5) - 2m^2/3m(m + 5) + (m + 5)
Factor out the common term m + 5
9/20m^3(m + 5) - 2m^2/(m + 5)(3m + 1)
Cross multiply
9(3m + 1) - (2 × 20)m^2m^3/20m^3(m + 5)(3m + 1)
Simplify 2 × 20 to 40
9(3m + 1) - 40m^2m^3/20m^3(m + 5)(3m + 1)
Use the Product Rule: x^ax^b = x^a + b
9(3m + 1) - 40m^2 + 3/ 20m^3(m + 5)(3m + 1)
Simplify 2 + 3 to 5
9(3m + 1) - 40m^5/20m^3(m + 5)(3m + 1)
Expand
[tex]\frac{27m+9-40m^5}{20m^3(m+5)(3m+1)}[/tex]
