Question

Solve for xx+8/(x+3)(x+4) = 3/x+3Correct equation with parenthesis:(x+8)/((x+3)(x+4)) = 3/(x+3)

Answer 1

Explanation

We must solve for x the following equation:

$\frac{x+8}{\left(x+3\right)\left(x+4\right)}=\frac{3}{x+3}.$

1) Assuming x ≠ -3 and x ≠ -4, we multiply both sides both sides by (x + 3)(x + 4):

$(x+8)=3\cdot(x+4).$

2) Applying the distribution property for the multiplication on the right side, we have:

$x+8=3x+12.$

3) Passing the x at the left as -x at the right, we have:

$\begin{gathered} 8=3x-x+12, \\ 8=2x+12. \end{gathered}$

4) Passing the +12 at the right as -12 at the left, we have:

$\begin{gathered} 8-12=2x, \\ -4=2x. \end{gathered}$

5) Finally, dividing both sides by 2, we get:

$x=-\frac{4}{2}=-2.$Answer

x = -2