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1/(3m)  +  (6m-9)/3m  = (3m-3)/4m

solve the equation??

 Nov 18, 2017
 #1
avatar+2340 
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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.
   
 Nov 18, 2017

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