Question

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

Answer 1

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 2

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;

• $\dfrac{2}{x^2 - 36} - \dfrac{1}{x^2+ 6 \cdot x} = \dfrac{2}{(x + 6) \cdot (x - 6)} - \dfrac{1}{x \cdot (x+ 6 )}$

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

x·(x + 6) = x·(x + a)

Therefore;

a = 6

• $\dfrac{2}{(x + 6) \cdot (x - 6)} - \dfrac{1}{x \cdot (x+ 6 )} = \dfrac{2 \cdot x }{(x + 6) \cdot (x - 6) \cdot x} - \dfrac{ (x - 6) }{x \cdot (x+ 6 )\cdot (x - 6) }$

By comparing the above expression, we have;

2·x = b·x

∴ b = 2

(x - 6) = (x - c)

∴ c = 6

• $\dfrac{2 \cdot x }{(x + 6) \cdot (x - 6) \cdot x} - \dfrac{ (x - 6) }{x \cdot (x+ 6 )\cdot (x - 6) } = \dfrac{2 \cdot x - x + 6}{(x + 6) \cdot (x - 6) \cdot x}$

By comparing, we have;

2·x - x + 6 = d·x - x + e

∴ d = 2, e = 6

• $\dfrac{2 \cdot x - x + 6}{(x + 6) \cdot (x - 6) \cdot x} = \dfrac{ x + 6}{(x + 6) \cdot (x - 6) \cdot x}$

Comparing gives;

x + 6 = x + f

f = 6

• $\dfrac{ x + 6}{(x + 6) \cdot (x - 6) \cdot x} = \dfrac{1}{ x\cdot (x - 6) } = \dfrac{g}{ x\cdot (x - 6) }$

Therefore; g = 1

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