Answer
$\displaystyle \frac{x}{2x-1}$
Work Step by Step
To subtract rational expressions with the same denominator,
subtract numerators and place the difference over the common denominator.
If possible, factor and simplify the result.
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Don't forget to place the second numerator in parentheses when subtracting.
$\displaystyle \frac{3x+1}{4x-2}-\frac{x+1}{4x-2}= \displaystyle \frac{3x+1-(x+1)}{4x-2}$
$= \displaystyle \frac{3x+1-x-1}{4x-2}$
$= \displaystyle \frac{2x}{4x-2}$
$=\displaystyle \frac{2(x)}{2(2x-1)}$
... reduce (divide the numerator and denominator with common factors)
$=\displaystyle \frac{x}{2x-1}$