how to solve (6a-24)/(2a^(2)+5a-12)*(4a^(2)-9)/(15a^(2)) step by step

Question

express each product in simples form.

Answer 1

[(6a-24)/(2a²-5a+12)][(4a²-9)/(15a²)]=[(6a-24)/(15a²)][(4a²-9)/(2a²+5a-12)].

Some factorisation is possible:

6a-24=6(a-4); 4a²-9=(2a-3)(2a+3); 2a²+5a-12=(a+4)(2a-3).

(6a-24)/(15a²)=6(a-4)/(15a²)=(6/15)(a-4)/a²=⅖(a-4)/a²;

(4a²-9)/(2a²+5a-12)=(2a-3)(2a+3)/(a+4)(2a-3)=(2a+3)/(a+4).

So we end up with:

⅖(a-4)(2a+3)/(a²(a+4)) or 2(a-4)(2a+3)/(5a²(a+4)).