Question

9/20m^4+100m^3-2m^2/3m^2+16m+5 =

Answer 1

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

$\frac{27m+9-40m^5}{20m^3(m+5)(3m+1)}$