$$\frac { 9 x - 8 } { 3 x + 5 } = \frac { 3 x - 5 } { x + 6 }$$
Solve for x
$x=\frac{1}{2}=0.5$
Steps for Solving Linear Equation
Variable $x$ cannot be equal to any of the values $-6,-\frac{5}{3}$ since division by zero is not defined. Multiply both sides of the equation by $\left(x+6\right)\left(3x+5\right)$, the least common multiple of $3x+5,x+6$.
Consider $\left(3x+5\right)\left(3x-5\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$. Square $5$.
$$9x^{2}+46x-48=\left(3x\right)^{2}-25$$
Expand $\left(3x\right)^{2}$.
$$9x^{2}+46x-48=3^{2}x^{2}-25$$
Calculate $3$ to the power of $2$ and get $9$.
$$9x^{2}+46x-48=9x^{2}-25$$
Subtract $9x^{2}$ from both sides.
$$9x^{2}+46x-48-9x^{2}=-25$$
Combine $9x^{2}$ and $-9x^{2}$ to get $0$.
$$46x-48=-25$$
Add $48$ to both sides.
$$46x=-25+48$$
Add $-25$ and $48$ to get $23$.
$$46x=23$$
Divide both sides by $46$.
$$x=\frac{23}{46}$$
Reduce the fraction $\frac{23}{46}$ to lowest terms by extracting and canceling out $23$.
