Question

Enter the values for the highlighted variables to complete the steps to find the sum: (see picture)

Answer 1

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

∵ $\frac{3x}{2x-6}+\frac{9}{6-2x}$ 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)

∴ $\frac{3x}{2x - 6}+\frac{9}{6-2x}=\frac{3x}{2x-6}+\frac{9}{-1(2x-6)}$

∴ a = -1

∵ 9 ÷ -1 = -9

∴ =  $\frac{3x}{2x-6}+\frac{-9}{2x-6}$

∴ b = -9

∵ The denominators of the two fractions are 2x - 6

∴ We can add them by adding their numerator

∵ 3x + -9 = 3x - 9

∴ = $\frac{3x-9}{2x-6}$

∴ 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)

∴ = $\frac{3(x-3)}{2(x-3)}$

∴ d = 3 , e = 3 , f = 2

- The fraction has same factor (x - 3) up and down then we can cancel

  them together

∴ = $\frac{3}{2}$

∴ g = 3/2