Often when solving linear equations we will need to work with an equation with fraction coefficients. We can solve these problems as we have in the past. This is demonstrated in our next example. Example

`3/4 x − 7/2 = 5/6`	Focus on subtraction
`3/4 x − 7/2+color(red)(7/2) = 5/6+color(red)(7/2)`	Add 7/2 to both sides
`3/4 x = 5/6+color(red)(21/6)`	Same problem, with common denominator 6
`3/4 x =26/6`	Solve right side
`3/4 x =13/3`	Reduce 26/6 to 13/3
`color(red)(4/3) 3/4 x=13/3color(red)(4/3) `	We can get rid of `3/4` by dividing both sides by `3/4`. Dividing by a fraction is the same as multiplying by the reciprocal, so we will multiply both sides by `4/3`.
`x=52/9 `	solution

Clear the fractions by finding the Largest Common Denominator(LCD) While this process does help us arrive at the correct solution, the fractions can make the process quite difficult. This is why we have an alternate method for dealing with fractions - clearing fractions. Clearing fractions is nice as it gets rid of the fractions for the majority of the problem. We can easily clear the fractions by finding the LCD and multiplying each term by the LCD. This is shown in the next example, the same problem as our first example, but this time we will solve by clearing fractions. Example ``

`3/4 x − 7/2 = 5/6`	`LCD = 12`, multiply each term by `12`
`color(red)(12)times3/4 x − color(red)(12)times7/2 = color(red)(12)times5/6`	Reduce each 12 with denominators
`color(red)(3)times3x − color(red)(6)times7 = color(red)(2)times5`	Multiply out each term
`9x−42=10`	Focus on subtraction by 42
`9x−42+color(red)(42)=10+color(red)(24)`	Add 42 to both sides
`9x=52`	Focus on multiplication by 9
`(9x)/color(red)(9)=52/color(red)(9) `	Divide both sides by 9
`x= 52/9`	Solution

The next example illustrates this as well. Notice the `2` isn’t a fraction in the original equation, but to solve it we put the `2` over `1` to make it a fraction. Example `2/3 x − 2 = 3/2 x + 1/6`

`2/3 x − 2 = 3/2 x + 1/6`	LCD = 6, multiply each term by 6
`color(red)(6)times2/3x − color(red)(6)times2/1 = (color(red)6)times3/2x + color(red)(6)times1/6`	Reduce 6 with each denominator
`color(red)(2)times2x − color(red)(6)times2 = color(red)(3)times3x + color(red)(1)times1`	Multiply out each term
`4x−12=9x+1`	Notice variable on both sides
`4xcolor(red)(-4x)-12=9xcolor(red)(-4x)+1`	Subtract `4x` from both sides
`−12=5x+1`	Focus on addition of `1`
`−12color(red)(-1)=5x+1color(red)(-1)`	Subtract `1` from both sides
`-13=5x`	Focus on multiplication of 5
`-13/color(red)5=(5x)/color(red)5`	Divide both sides by 5
`-13/5=x`	Solution