Answer
$\displaystyle \frac{3x+1}{7x-3}$
Work Step by Step
.... When one denominator is the opposite, or additive inverse of the other,
first multiply either rational expression by $\displaystyle \frac{-1}{-1}$
to obtain a common denominator.
$\displaystyle \frac{9x-1}{7x-3}+\frac{6x-2}{3-7x}\cdot \displaystyle \frac{-1}{-1} = \displaystyle \frac{9x-1}{7x-3}+ \frac{-6x+2}{7x-3}$
... To add/subtract rational expressions with the same denominator,
add/subtract numerators and
place the sum/difference over the common denominator.
If possible, factor and simplify the result.
$= \displaystyle \frac{9x-1-6x+2}{7x-3}$
$= \displaystyle \frac{3x+1}{7x-3}$
