Question

PLEASE HELP
What is the solution of x^2-1/x^2+5x+4
Only give an answer as shown in the picture please.

Answer 1

$\\ \sf\longmapsto \dfrac{x^2-1}{x^2+5x+4}\leqslant 0$

• Solving denominator

$\\ \sf\longmapsto x^2+5x+4>0$

$\\ \sf\longmapsto x^2+4x+x+4>0$

$\\ \sf\longmapsto x(x+4)+1(x+4)>0$

$\\ \sf\longmapsto (x+4)(x+1)>0$

$\\ \sf\longmapsto x>-4\:or x>-1$

• Hence x$\neq$-1
• x can't be 0 as it makes function undefined

$\\ \sf\longmapsto -4<x\leqslant 1,x\neq -1$