I don't know if you just wanted to solve the equation, or if you wanted to see the steps that one might do by hand. In any case, I'm going to show how one might do this for this simple equation.
Mathematica automatically removes common factors from the numerator and denominator of fractions. So if you want to show that, you have to take extra measures but first let's go with it and show the remaining steps.
Here we annotate the steps with Print statements. We manipulate the equation by using a Pure Function (look up Function in Help) to map the same operation onto both sides of the equation. So the # stands in for each side of the equation. "/@" represents the Map function.
Print["Original Equation. Mathematica reduces fractions."]
step1 = 3 r + 6/9 == 4 r - 24/4
Print["Consolidate r on the right hand side."]
step2 = # - 3 r & /@ step1
Print["Add 6 to both sides."]
step3 = # + 6 & /@ step2
Print["Reverse the equation."]
Reverse[step3]
Now let's do it using symbolic fractions and substituting at the end. We'll just add a to the numbers to turn them into symbols.
Print["Original Equation with symbolic fractions."]
step1 = 3 r + a6/a9 == 4 r - a24/a4
Print["Clear the denominators on both sides of the equation."]
step2 = Distribute[# a9 a4] & /@ step1
Print["Move the rhs r term to the lhs and the lhs constant to the \
rhs."]
step3 = # - 4 a4 a9 r - a4 a6 & /@ step2
Print["Divide each side by the r coefficient."]
step4 = Distribute[#/(-a4 a9)] & /@ step3
Print["Substitute the fraction values."]
step4 /. {a4 -> 4, a6 -> 6, a9 -> 9, a24 -> 24}
We really didn't learn much by keeping tract of the numerators and denominators. We might just have used two symbols.
You can copy and paste the above code into your Mathematica notebook and evaluate or download the attached notebook.
Attachments: