Variable $x$ cannot be equal to $-2$ since division by zero is not defined. Divide $1$ by $\frac{9+5x}{2+x}$ by multiplying $1$ by the reciprocal of $\frac{9+5x}{2+x}$.
$$19.3+\frac{2+x}{9+5x}=2$$
Subtract $19.3$ from both sides.
$$\frac{2+x}{9+5x}=2-19.3$$
Subtract $19.3$ from $2$ to get $-17.3$.
$$\frac{2+x}{9+5x}=-17.3$$
Variable $x$ cannot be equal to $-\frac{9}{5}$ since division by zero is not defined. Multiply both sides of the equation by $5x+9$.
$$2+x=-17.3\left(5x+9\right)$$
Use the distributive property to multiply $-17.3$ by $5x+9$.
$$2+x=-86.5x-155.7$$
Add $86.5x$ to both sides.
$$2+x+86.5x=-155.7$$
Combine $x$ and $86.5x$ to get $87.5x$.
$$2+87.5x=-155.7$$
Subtract $2$ from both sides.
$$87.5x=-155.7-2$$
Subtract $2$ from $-155.7$ to get $-157.7$.
$$87.5x=-157.7$$
Divide both sides by $87.5$.
$$x=\frac{-157.7}{87.5}$$
Expand $\frac{-157.7}{87.5}$ by multiplying both numerator and the denominator by $10$.
$$x=\frac{-1577}{875}$$
Fraction $\frac{-1577}{875}$ can be rewritten as $-\frac{1577}{875}$ by extracting the negative sign.
