Answer:
Explanation:
We are given two fractions:
(3y + 9)/(2y - 13) and (2y - 13)/(2y + 5)
We are also given that the sum of these fractions is 2:
(3y + 9)/(2y - 13) + (2y - 13)/(2y + 5) = 2
To solve for y, we can first simplify the left side of the equation by finding a common denominator:
[(3y + 9)(2y + 5) + (2y - 13)(2y - 13)] / [(2y - 13)(2y + 5)] = 2
Simplifying the numerator:
[6y^2 + 27y - 39] / [(2y - 13)(2y + 5)] = 2
Multiplying both sides by the denominator:
6y^2 + 27y - 39 = 2(2y - 13)(2y + 5)
Expanding the right side:
6y^2 + 27y - 39 = 8y^2 - 66y - 130
Moving all terms to one side:
2y^2 - 93y + 91 = 0
We can now use the quadratic formula to solve for y:
y = [-(-93) ± sqrt((-93)^2 - 4(2)(91))] / (2(2))
y = [93 ± sqrt(8641)] / 4
y ≈ 12.66 or y ≈ 1.59
So there are two possible values for y that satisfy the equation.