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The common denominator of the two fractions is: 12

$ \frac{(x-2)}{3 }= \frac{(4*(x-2))}{(3*4)} = \frac{(4*(x-2))}{12} $

$ \frac{(x-2)}{4 }= \frac{(3*(x-2))}{(3*4)} = \frac{(3*(x-2))}{12} $

Fractions adjusted to a common denominator

$ \frac{(x-2)}{3 }+ \frac{(x-2)}{4 }= \frac{(4*(x-2))}{12 }+ \frac{(3*(x-2))}{12} $

$ \frac{(4*(x-2))}{12 }+ \frac{(3*(x-2))}{12 }= \frac{(4*(x-2)+3*(x-2))}{12} $

$ \frac{(4*(x-2)+3*(x-2))}{12 }= \frac{(4*(x-2)+3*(x-2))}{12} $

$ $

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