1/(3m)  +  (6m-9)/3m  = (3m-3)/4m

solve the equation??

Guest Nov 18, 2017

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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