Sometimes, you may have a problem that contains fractions as coefficients or constants. You are allowed to leave them as they are and apply the basic rules of algebra to solve the problem. However, using the distributive property can often simplify the solution by turning the fractions into integers. Consider the example x−3=x3+16{\displaystyle x-3={\frac {x}{3}}+{\frac {1}{6}}}. The fractions in this problem are x3{\displaystyle {\frac {x}{3}}} and 16{\displaystyle {\frac {1}{6}}}. For this step, you can ignore all the integers. Look only at the fractions, and find the LCM for all the denominators. To find the LCM, you need the smallest number that is evenly divisible by the denominators of the fractions in the equation. In this example, the denominators are 3 and 6, so the LCM is 6. Remember that you can perform any operation that you want to an algebra equation, as long as you do it equally to both sides. Multiply all terms of the equation by the LCM, and the fractions will cancel out and “become” integers. Place parentheses around the entire left and right sides of the equation and then perform the distribution:   x−3=x3+16{\displaystyle x-3={\frac {x}{3}}+{\frac {1}{6}}}…..(original equation)  (x−3)=(x3+16){\displaystyle (x-3)=({\frac {x}{3}}+{\frac {1}{6}})}…..(insert parentheses)  6(x−3)=6(x3+16){\displaystyle 6(x-3)=6({\frac {x}{3}}+{\frac {1}{6}})}…..(multiply both sides by LCM)  6x−6(3)=6(x3)+6(16){\displaystyle 6x-6(3)=6({\frac {x}{3}})+6({\frac {1}{6}})}…..(distribute multiplication)  6x−18=2x+1{\displaystyle 6x-18=2x+1}…..(simplify multiplication) Combine all of the terms so all the variables appear on one side of the equation, and all constants appear on the other. Use basic operations of addition and subtraction to move terms from one side to the other.   6x−18=2x+1{\displaystyle 6x-18=2x+1}…..(simplified problem)  6x−2x−18=2x−2x+1{\displaystyle 6x-2x-18=2x-2x+1}…..(subtract 2x from both sides)  4x−18=1{\displaystyle 4x-18=1}…..(simplify subtraction)  4x−18+18=1+18{\displaystyle 4x-18+18=1+18}…..(add 18 to both sides)  4x=19{\displaystyle 4x=19}…..(simplify addition) Find the final solution by dividing both sides of the equation by the coefficient of the variable. This should leave a single x term on one side of the equation, and the numerical solution on the other.   4x=19{\displaystyle 4x=19}…..(revised problem)  4x/4=19/4{\displaystyle 4x/4=19/4}…..(divide both sides by 4)  x=194 or 434{\displaystyle x={\frac {19}{4}}{\text{ or }}4{\frac {3}{4}}}…..(final solution)
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