We must solve for x the following equation:
[tex]\frac{x+8}{\left(x+3\right)\left(x+4\right)}=\frac{3}{x+3}.[/tex]1) Assuming x ≠ -3 and x ≠ -4, we multiply both sides both sides by (x + 3)(x + 4):
[tex](x+8)=3\cdot(x+4).[/tex]2) Applying the distribution property for the multiplication on the right side, we have:
[tex]x+8=3x+12.[/tex]3) Passing the x at the left as -x at the right, we have:
[tex]\begin{gathered} 8=3x-x+12, \\ 8=2x+12. \end{gathered}[/tex]4) Passing the +12 at the right as -12 at the left, we have:
[tex]\begin{gathered} 8-12=2x, \\ -4=2x. \end{gathered}[/tex]5) Finally, dividing both sides by 2, we get:
[tex]x=-\frac{4}{2}=-2.[/tex]Answerx = -2
