To find the sum of the given expression, we need to solve the equation first. Let's go through the steps to find the sum:
Step 1: Rewrite the equation with the highlighted variables:
(3x)/(2x-6) + (9)/(6-2x) = (3x)/(2x-6) + (9)/(a(2x-6))
Step 2: Find a common denominator for the fractions. The common denominator is (2x - 6):
(3x)/(2x-6) + (9)/(6-2x) = (3x)/(2x-6) + (9)/(a(2x-6))
Step 3: Multiply each fraction by the common denominator to eliminate the denominators:
(3x)(a(2x-6))/(2x-6) + (9)(2x-6)/(6-2x) = (3x)(a(2x-6))/(2x-6) + (9)/(a(2x-6))
Step 4: Distribute and simplify:
(6ax^2 - 18ax) + (18x - 54) = (6ax^2 - 18ax) + (9)/(a(2x-6))
Step 5: Combine like terms on both sides of the equation:
6ax^2 - 18ax + 18x - 54 = 6ax^2 - 18ax + (9)/(a(2x-6))
Step 6: Subtract (6ax^2 - 18ax) from both sides:
18x - 54 = (9)/(a(2x-6))
Step 7: Multiply both sides by a(2x-6) to eliminate the denominator on the right side:
(a(2x-6))(18x - 54) = 9
Step 8: Distribute and simplify:
18ax^2 - 54ax - 108ax + 324 = 9
Step 9: Combine like terms:
18ax^2 - 162ax + 324 = 9
Step 10: Subtract 9 from both sides:
18ax^2 - 162ax + 315 = 0
Now, you can use this quadratic equation to solve for the variable "x".