hi
Here i am showing the answer of the first problem, the the other guy he showed to how to frame the problem that's fantastic way , i will do the remaining steps to show the answers here
7x+4=A(x+2)^2+B(x+2)(x-3)+c(x-3)
plug x=3 in the above equation u will get
25A=25
then A=1
plug x=-2, then C=2
finally equating the coefficient of x^2 on both sides we get it as
A+B=0
B=-1
=1/(x-3)-1/(x+2)+2/(x+2)^2 is the final answer