Subtract the rational expressions x^2/2x−12−18/x−6. Simplify the answer.
Responses
x+6/2
the fraction with numerator x plus 6 and denominator 2 -this is the correct answer
x−6/2
the fraction with numerator x minus 6 and denominator 2 -incorrect
x^2−18/x−6
the fraction with numerator x squared minus 18 and denominator x minus 6 -incorrect
x^2−36/2(x−6) -incorrect
explain how you would get that as your correct answer x+6/2
To subtract rational expressions, you need to have a common denominator for both fractions.
In this case, the common denominator is 2(x-6).
To find the numerator of the simplified expression, you can use the cross-multiplication method.
The numerator of the difference of the rational expressions would be:
(x^2)(2) - (18)(2)
Expanding this, you get:
2x^2 - 36
So, the simplified answer is (2x^2 - 36)/(2x - 12).
To further simplify it, you can factor out the common factor of 2 from both the numerator and denominator:
2(x^2 - 18)/(2(x - 6))
This simplifies to:
(x^2 - 18)/(x - 6)
Thus, the correct answer is (x^2 - 18)/(x - 6).