Answer: The simplified form will be
[tex]\frac{1}{(x+3)(x+4)}[/tex]
Step-by-step explanation:
Since we have given that
[tex]\frac{x+1}{x^2+x-6}\div \frac{x^2+5x+4}{x-2}[/tex]
We need to simplify the above expression, we get that
[tex]\frac{x+1}{x^2+x-6}\div \frac{x^2+5x+4}{x-2}\\\\=\frac{x+1}{x^2+x-6}\times \frac{x-2}{x^2+5x+4}\\[/tex]
Now, we first factorize the quadratic equation:
[tex]x^2+x-6\\\\=x^2+3x-2x-6\\\\=x(x+3)-2(x-3)\\\\=(x+3)(x-2)[/tex]
Similarly,
[tex]x^2+5x+4\\\\=x^2+4x+x+4\\\\=x(x+4)+1(x+4)\\\\=(x+4)(x+1)[/tex]
So, it will become
[tex]\frac{x+1}{x^2+x-6}\times \frac{x-2}{x^2+5x+4}\\\\=\frac{x+1}{(x+3)(x-2)}\times \frac{x-2}{(x+4)(x+1)}\\\\=\frac{1}{(x+3)(x+4)}[/tex]
Hence, the simplified form will be
[tex]\frac{1}{(x+3)(x+4)}[/tex]
