Solve (a+2)(a+3)/3(a+2)=4(a+3)/x

$$\frac { ( a + 2 ) ( a + 3 ) } { 3 ( a + 2 ) } = \frac { 4 ( a + 3 ) } { x }$$

Solve for x

$$\left\{\begin{matrix}x=12\text{, }&a\neq -2\\x\neq 0\text{, }&a=-3\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3x\left(a+2\right), the least common multiple of 3\left(a+2\right),x.

$$x\left(a+2\right)\left(a+3\right)=\left(3a+6\right)\times 4\left(a+3\right)$$

Use the distributive property to multiply x by a+2.

$$\left(xa+2x\right)\left(a+3\right)=\left(3a+6\right)\times 4\left(a+3\right)$$

Use the distributive property to multiply xa+2x by a+3 and combine like terms.

$$xa^{2}+5xa+6x=\left(3a+6\right)\times 4\left(a+3\right)$$

Use the distributive property to multiply 3a+6 by 4.

$$xa^{2}+5xa+6x=\left(12a+24\right)\left(a+3\right)$$

Use the distributive property to multiply 12a+24 by a+3 and combine like terms.

$$xa^{2}+5xa+6x=12a^{2}+60a+72$$

Combine all terms containing x.

$$\left(a^{2}+5a+6\right)x=12a^{2}+60a+72$$

Divide both sides by a^{2}+5a+6.

$$\frac{\left(a^{2}+5a+6\right)x}{a^{2}+5a+6}=\frac{12\left(a+2\right)\left(a+3\right)}{a^{2}+5a+6}$$

Dividing by a^{2}+5a+6 undoes the multiplication by a^{2}+5a+6.

$$x=\frac{12\left(a+2\right)\left(a+3\right)}{a^{2}+5a+6}$$

Divide 12\left(2+a\right)\left(3+a\right) by a^{2}+5a+6.

$$x=12$$

Solve for a

$$\left\{\begin{matrix}a=-3\text{, }&x\neq 0\\a\neq -2\text{, }&x=12\end{matrix}\right.$$