Simplify 3/(x-2)+5/(2-x)

Problem

3/(x−2)+5/(2−x)

Solution

1. Identify the denominators in the expression, which are x−2 and 2−x

2. Rewrite the second denominator by factoring out a negative sign so that the denominators match: $2-x = -(x-2)$.

3. Substitute this into the expression:

3/(x−2)+5/(−(x−2))

4. Move the negative sign from the denominator to the numerator:

3/(x−2)−5/(x−2)

5. Combine the fractions since they now have a common denominator:

(3−5)/(x−2)

6. Simplify the numerator:

(−2)/(x−2)

Final Answer

3/(x−2)+5/(2−x)=(−2)/(x−2)

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