Answer:
a = -1
b = -9
c = 9
d = 3
e = 3
f = 2
g = 3/2
Step-by-step explanation:
* Lets explain how to solve the problem
∵ [tex]\frac{3x}{2x-6}+\frac{9}{6-2x}[/tex] are rational fractions
- To add or subtract the rational fractions they must have same
denominator
∵ 6 - 2x must be written 2x - 6, take (-1) as a common factor from 6 - 2x
∴ - 1(-6 + 2x) = - 1(2x - 6)
∴ [tex]\frac{3x}{2x - 6}+\frac{9}{6-2x}=\frac{3x}{2x-6}+\frac{9}{-1(2x-6)}[/tex]
∴ a = -1
∵ 9 ÷ -1 = -9
∴ = [tex]\frac{3x}{2x-6}+\frac{-9}{2x-6}[/tex]
∴ b = -9
∵ The denominators of the two fractions are 2x - 6
∴ We can add them by adding their numerator
∵ 3x + -9 = 3x - 9
∴ = [tex]\frac{3x-9}{2x-6}[/tex]
∴ c = 9
∵ 3x - 9 has a common factor 3
∴ 3x - 9 = 3(x - 3)
∵ 2x - 6 has common factor 2
∴ 2x - 6 = 2(x - 3)
∴ = [tex]\frac{3(x-3)}{2(x-3)}[/tex]
∴ d = 3 , e = 3 , f = 2
- The fraction has same factor (x - 3) up and down then we can cancel
them together
∴ = [tex]\frac{3}{2}[/tex]
∴ g = 3/2
