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

Step-by-step explanation

We must solve for x the following equation:

`(x+8)/(\left(x+3\right)\left(x+4\right))=(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=-(4)/(2)=-2.`Answer

x = -2