$$\frac { 2 a + ( 9 + 3 a ) } { 3 a - ( 3 + 2 a ) } = \frac { 5 } { 6 }$$
Solve for a
$a = -\frac{69}{25} = -2\frac{19}{25} = -2.76$
Steps for Solving Linear Equation
Variable $a$ cannot be equal to $3$ since division by zero is not defined. Multiply both sides of the equation by $6\left(a-3\right)$, the least common multiple of $3a-\left(3+2a\right),6$.
$$6\left(2a+9+3a\right)=5\left(a-3\right)$$
Combine $2a$ and $3a$ to get $5a$.
$$6\left(5a+9\right)=5\left(a-3\right)$$
Use the distributive property to multiply $6$ by $5a+9$.
$$30a+54=5\left(a-3\right)$$
Use the distributive property to multiply $5$ by $a-3$.
$$30a+54=5a-15$$
Subtract $5a$ from both sides.
$$30a+54-5a=-15$$
Combine $30a$ and $-5a$ to get $25a$.
$$25a+54=-15$$
Subtract $54$ from both sides.
$$25a=-15-54$$
Subtract $54$ from $-15$ to get $-69$.
$$25a=-69$$
Divide both sides by $25$.
$$a=\frac{-69}{25}$$
Fraction $\frac{-69}{25}$ can be rewritten as $-\frac{69}{25}$ by extracting the negative sign.
