Enter the values for the highlighted variables that show how to subtract the rational expressions correctly

a = 6
x^2 + 6x is equal to x(x+6)
b=2
Denominator and numerator of the first term are multiplied by x.
c=6
Second term is multiplied by (x-6)/(x-6)
d=2
Now that they have the same denominator, the two terms are combined. 2 is the coefficient of the first term
e=6
In the same way as d is carried over from b, e is carried over from c.
f = 6
2x - x + 6 = x + 6
g = 1
We factor out the (x+6) from the numerator and denominator

Answer Link

oeerivona oeerivona · Answer 2 · 2021-11-02T16:39:33+01:00

The values of the highlighted variables can be obtained by comparing the

results of the steps of the subtraction process.

The values are;

a = 6

b = 2

c = 6

d = 2

e = 6

f = 6

g = 1

Reasons:

The given rational expression is presented as follows;

[tex]\dfrac{2}{x^2 - 36} - \dfrac{1}{x^2+ 6 \cdot x} = \dfrac{2}{(x + 6) \cdot (x - 6)} - \dfrac{1}{x \cdot (x+ 6 )}[/tex]

By comparing the above equation, to the question, we have;

x·(x + 6) = x·(x + a)

Therefore;

a = 6

[tex]\dfrac{2}{(x + 6) \cdot (x - 6)} - \dfrac{1}{x \cdot (x+ 6 )} = \dfrac{2 \cdot x }{(x + 6) \cdot (x - 6) \cdot x} - \dfrac{ (x - 6) }{x \cdot (x+ 6 )\cdot (x - 6) }[/tex]

By comparing the above expression, we have;

2·x = b·x

∴ b = 2

(x - 6) = (x - c)

∴ c = 6

[tex]\dfrac{2 \cdot x }{(x + 6) \cdot (x - 6) \cdot x} - \dfrac{ (x - 6) }{x \cdot (x+ 6 )\cdot (x - 6) } = \dfrac{2 \cdot x - x + 6}{(x + 6) \cdot (x - 6) \cdot x}[/tex]

By comparing, we have;

2·x - x + 6 = d·x - x + e

∴ d = 2, e = 6

[tex]\dfrac{2 \cdot x - x + 6}{(x + 6) \cdot (x - 6) \cdot x} = \dfrac{ x + 6}{(x + 6) \cdot (x - 6) \cdot x}[/tex]

Comparing gives;

x + 6 = x + f

f = 6

[tex]\dfrac{ x + 6}{(x + 6) \cdot (x - 6) \cdot x} = \dfrac{1}{ x\cdot (x - 6) } = \dfrac{g}{ x\cdot (x - 6) }[/tex]

Therefore; g = 1

Learn more here:

https://brainly.com/question/6238511

https://brainly.com/question/22241816

https://brainly.com/question/9353162