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# HELP

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1/(3m)  +  (6m-9)/3m  = (3m-3)/4m

solve the equation??

Guest Nov 18, 2017
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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

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