The sum of the variables in the equation is 8.5
To obtain 'a' :
Factorize 6 - 2x such that it has a factor of 2x - 6
To do this , multiply (6 - 2x) by -1
-1 * (6 - 2x) = 2x - 6
Hence, 'a' = -1
To get the value of 'b' :
By multiplying the numerator and denominator by -1 , we get rid of -1 in the denominator,
Now we have :
3x/(2x - 6) + 9/-1(2x - 6) = 3x/(2x - 6) + (-9)/(2x - 6)
Hence, b = -9
To obtain 'c'
3x/(2x - 6) + (-9)/(2x - 6)
L.C.M is (2x - 6)
3x - 9 /2x - 6
Hence, c = 9
To obtain 'd', 'e' and 'f' :
Factorize 3x - 9 /2x - 6
3(x - 3)/2(x - 3)
comparing the expression :
d = 3 ; e = 3 ; f = 2
To obtain 'g' :
3(x - 3)/2(x - 3) = 3/2
Hence, g = 3/2
Sum of the variables:
-1 + (-9) + 9 + 3 + 3 + 2 + 3/2
-1 - 9 + 9 + 3 + 3 + 2 + 3/2
= 8.5