How do you simplify #(3a^2-ab-2b^2)/(a^3b^3 )÷ (15a^2+10ab)/(5a^2+5ab+10b^2)#?

Question

Ethan Adkins · Accepted Answer

=#((a-b)(3a^2 +ab+2b^2))/(a^4b^3)#

#(3a^2-ab-2b^2)/(a^3b^3 )÷ (15a^2+10ab)/(5a^2+5ab+10b^2)#

Factorise wherever possible:

#((3a+2b)(a-b))/(a^3b^3 )xx (5(3a^2 +ab+2b^2))/(5a(3a+2b))#

#(cancel((3a+2b))(a-b))/(a^3b^3 )xx (cancel5(3a^2 +ab+2b^2))/(cancel5a(cancel(3a+2b))#

=#((a-b)(3a^2 +ab+2b^2))/(a^4b^3)#

Eva Adamson · Answer

undefined To simplify the expression (3a^2-ab-2b^2)/(a^3b^3) ÷ (15a^2+10ab)/(5a^2+5ab+10b^2), we can follow these steps:

1. Simplify the numerator and denominator separately:
   - In the numerator, we have (3a^2 - ab - 2b^2).
   - In the denominator, we have (a^3b^3).

2. Divide the numerator by the denominator:
   - Divide (3a^2 - ab - 2b^2) by (a^3b^3).

3. Simplify the second fraction:
   - Simplify (15a^2 + 10ab) / (5a^2 + 5ab + 10b^2).

Combining these steps, the simplified expression is:
(3a^2 - ab - 2b^2) / (a^3b^3) ÷ (15a^2 + 10ab) / (5a^2 + 5ab + 10b^2)