Answer:
The function is given by,
f(x)=
x
2
+x−2
2x−3
The function is represented as, f(x)=
q(x)
p(x)
where, p(x)=2x−3 and q(x)=x
2
+x−2
Domain of the function is given as,
dom[f(x)]=R−{x:q(x)=0}
Put q(x)=0
∴x
2
+x−2=0
∴x
2
+2x−x−2=0
∴x(x+2)−1(x+2)=0
∴(x+2)(x−1)=0
∴x+2=0 or x−1=0
∴x=−2 or x=1
Thus, domain of the function is,
dom[f(x)]=R−{−2,1}