Simplify (3y)/(2y-6)+9/(6-2y)

Problem

(3*y)/(2*y−6)+9/(6−2*y)

Solution

1. Identify the denominators in the expression, which are 2*y−6 and 6−2*y

2. Factor the constant −1 from the second denominator to see the relationship between the two terms.

6−2*y=−1*(2*y−6)

3. Rewrite the second fraction using this factored form to create a common denominator.

9/(6−2*y)=9/(−1*(2*y−6))=−9/(2*y−6)

4. Combine the two fractions now that they share the common denominator 2*y−6

(3*y)/(2*y−6)−9/(2*y−6)=(3*y−9)/(2*y−6)

5. Factor the numerator and the denominator to check for common factors.

3*y−9=3*(y−3)

2*y−6=2*(y−3)

6. Cancel the common factor (y−3) from the numerator and the denominator, assuming y≠3

(3*(y−3))/(2*(y−3))=3/2

Final Answer

(3*y)/(2*y−6)+9/(6−2*y)=3/2

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