how to solve 2x^2-3x-2 divided by x+2.x^2-4 divided by 2x+1

Question

how to divide this 2 terms

Answer 1

2x²-3x-2=(x-2)(2x+1); x²-4=(x-2)(x+2).

(2x²-3x-2)/(2x+1)=x-2;

(2x²-3x-2)/(2x+1)/(x-2)=(x-2)/(x-2)=1;

1/(x+2).(1/(x+2))=1/(x+2)².

(2x²-3x-2)/[(x+2)(x²-4)]/(2x+1)=[(x-2)(2x+1)/(2x+1)]/[(x+2)(x-2)(x+2)]=1/(x+2)².