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#1**+2 **

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. |

TheXSquaredFactor Nov 18, 2017