T2 3ar 10ar2 3T 4 0 Solutionx23x10x23x40 x25x2x10x24xx40 xx5

Solution

(x²+3x-10)/(x²+3x-4)>0

(x²+5x-2x-10)/(x²+4x-x-4)>0

(x(x+5)-2(x+5))/(x(x+4)-1(x+4))>0

((x+5)(x-2))/((x+4)(x-1))>0

equality is not defined if denominator =0

domain is all real numbers except x =-4 ,x=1

when x<-5, ((x+5)(x-2))/((x+4)(x-1)) >0

-5<x<-4 , ((x+5)(x-2))/((x+4)(x-1)) <0

-4<x<1, ((x+5)(x-2))/((x+4)(x-1)) >0

1<x<2, ((x+5)(x-2))/((x+4)(x-1)) <0

x>0 , ((x+5)(x-2))/((x+4)(x-1)) >0

so x =(-infinity,-5)U(-4,1)U(0,infinity)