Add 5/(x-y)+9/(y-x)+4/(x-y)

Problem

5/(x−y)+9/(y−x)+4/(x−y)

Solution

1. Identify the denominators in the expression. The denominators are x−y and y−x

2. Rewrite the second denominator to find a common denominator. Since y−x=−(x−y) the second term can be rewritten by moving the negative sign to the numerator.

9/(y−x)=9/(−(x−y))=−9/(x−y)

3. Substitute the rewritten term back into the original expression.

5/(x−y)−9/(x−y)+4/(x−y)

4. Combine the numerators over the common denominator x−y

(5−9+4)/(x−y)

5. Simplify the numerator by performing the addition and subtraction.

5−9+4=0

6. Evaluate the final fraction. Since the numerator is zero and the denominator is non-zero (assuming x≠y, the entire expression equals zero.

0/(x−y)=0

Final Answer

5/(x−y)+9/(y−x)+4/(x−y)=0

Want more problems? Check here!