The values for the highlighted variables are: a = -1, b = 9, c = 9, d = 3, e = 3, f = 2 and g = 1.5. And the sum of the variables is equal to 26.5.
Given :
Equation - [tex]\dfrac{3x}{2x-6}+\dfrac{9}{6-2x}[/tex]
Taking -1 common from (6-2x) in the above equation:
[tex]\dfrac{3x}{2x-6}+\dfrac{9}{6-2x} = \dfrac{3x}{2x-6}+\dfrac{9}{-1(2x-6)}[/tex] ---- (1)
By compairing the above equation with the given data, the value of a = -1 and b = 9.
Now, further simplify equation (1).
[tex]\dfrac{3x}{2x-6}+\dfrac{9}{6-2x} = \dfrac{(3x-9)}{(2x-6)}[/tex] ---- (2)
By compairing the above equation with the given data, the value of c = 9.
Now, from equation (2) taking 2 common from the denominator and taking 3 common from the numerator.
[tex]\dfrac{3x}{2x-6}+\dfrac{9}{6-2x} = \dfrac{3(x-3)}{2(x-3)}[/tex] ----- (3)
By compairing the above equation with the given data, the value of d = 3, e = 3 and f = 2.
Now, from equation (3), (x-3) will be cancel out.
[tex]\dfrac{3x}{2x-6}+\dfrac{9}{6-2x} = \dfrac{3}{2}[/tex]
By compairing the above equation with the given data, the value of g = 1.5.
The sum of the unknown variables = a + b + c + d + e + f + g
= -1+9+9+3+3+2+1.5 = 26.5
For more information, refer the link given below
https://brainly.com/question/12420841
