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 (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
  `\\eq`-1
• x can't be 0 as it makes function undefined

`\\ \sf\longmapsto -4<x\leqslant 1,x\\eq -1`