Solve the inequality and write your answer in interval notation.

I have done another version of the graph    

I have just done this really to demonstrate another feature of Desmos Graphing calculator :)

https://www.desmos.com/calculator/ls50nnme3r

The expression is less than 0 for -4<x<-1 and 0<x<1

x^2+3x-4

_________<0

x^2+x

This is a kinda' funky one....!!!!!

Factoring the denominator, we have x(x+1)  which means that we will have  vertiical asymptotes at x = -1 and x = 0

Factoring the numerator, we have (x +4)(x - 1) < 0

Setting each factor to 0, we have x = -4 and x = 1     .....so.....

Our possible answers come from these intervals (-∞, -4) (-4, -1) (-1, 0) (0, 1) (1, ∞)

Look at the graph, here.......https://www.desmos.com/calculator/fmhvy1d7ke

This rational function is >0 on these intervals (-∞, -4)  (-1, 0)  and  (1, ∞)

And it is < 0 on (-4, -1)  and (0, 1)