Variable $x$ cannot be equal to any of the values $-4,-3,-2$ since division by zero is not defined. Multiply both sides of the equation by $\left(x+2\right)\left(x+3\right)\left(x+4\right)$, the least common multiple of $x^{2}+7x+12,x^{2}+5x+6,x^{2}+6x+8$.
$$x+2+x+4=\left(x+3\right)\times 2$$
Combine $x$ and $x$ to get $2x$.
$$2x+2+4=\left(x+3\right)\times 2$$
Add $2$ and $4$ to get $6$.
$$2x+6=\left(x+3\right)\times 2$$
Use the distributive property to multiply $x+3$ by $2$.
$$2x+6=2x+6$$
Subtract $2x$ from both sides.
$$2x+6-2x=6$$
Combine $2x$ and $-2x$ to get $0$.
$$6=6$$
Compare $6$ and $6$.
$$\text{true}$$
This is true for any $x$.
$$x\in \mathrm{C}$$
Variable $x$ cannot be equal to any of the values $-4,-3,-2$.
Variable $x$ cannot be equal to any of the values $-4,-3,-2$ since division by zero is not defined. Multiply both sides of the equation by $\left(x+2\right)\left(x+3\right)\left(x+4\right)$, the least common multiple of $x^{2}+7x+12,x^{2}+5x+6,x^{2}+6x+8$.
$$x+2+x+4=\left(x+3\right)\times 2$$
Combine $x$ and $x$ to get $2x$.
$$2x+2+4=\left(x+3\right)\times 2$$
Add $2$ and $4$ to get $6$.
$$2x+6=\left(x+3\right)\times 2$$
Use the distributive property to multiply $x+3$ by $2$.
$$2x+6=2x+6$$
Subtract $2x$ from both sides.
$$2x+6-2x=6$$
Combine $2x$ and $-2x$ to get $0$.
$$6=6$$
Compare $6$ and $6$.
$$\text{true}$$
This is true for any $x$.
$$x\in \mathrm{R}$$
Variable $x$ cannot be equal to any of the values $-4,-3,-2$.
