+2446 Before starting to solve this particular question, take note of any potential extraneous solutions.
\(m\neq0\) because that will result in division by zero, which would not be a valid solution to this equation.
| \(\frac{1}{3m}+\frac{6m-9}{3m}=\frac{3m-3}{4m}\) | The terms on the left hand side are both like terms and can be combined. |
| \(\frac{6m-8}{3m}=\frac{3m-3}{4m}\) | Now, multiply by the LCM, 12m in this case, of the denominators to eliminate the fractions. |
| \(\frac{12m(6m-8)}{3m}=\frac{12m(3m-3)}{4m}\) | Simplify both sides now. |
| \(4(6m-8)=3(3m-3)\) | Distribute on both sides. |
| \(24m-32=9m-9\) | Subtract 9m from both sides. |
| \(15m-32=-9\) | Add 32 to both sides. |
| \(15m=23\) | Divide by 15 from both sides of the equation. |
| \(m=\frac{23}{15}\) | This solution does not match a predetermined extraneous solution, so this is a valid solution. |
