Variable $x$ cannot be equal to any of the values $-5,-\frac{3}{2}$ since division by zero is not defined. Multiply both sides of the equation by $\left(x+5\right)\left(2x+3\right)$, the least common multiple of $2x+3,x+5$.
$$x+5=\left(2x+3\right)\times 3$$
Use the distributive property to multiply $2x+3$ by $3$.
$$x+5=6x+9$$
Subtract $6x$ from both sides.
$$x+5-6x=9$$
Combine $x$ and $-6x$ to get $-5x$.
$$-5x+5=9$$
Subtract $5$ from both sides.
$$-5x=9-5$$
Subtract $5$ from $9$ to get $4$.
$$-5x=4$$
Divide both sides by $-5$.
$$x=\frac{4}{-5}$$
Fraction $\frac{4}{-5}$ can be rewritten as $-\frac{4}{5}$ by extracting the negative sign.
