Question

What is the difference of the rational expessions below? 6/x - 5x/x+2

Answer 1

B

Explanation:

You want the difference of the rational expressions (6/x) and (5x/(x+2)).

Difference

The difference of rational expressions is found the same way any difference of fractions is found. The fractions are written using a common denominator, and the difference is taken of the numerators.

`(6)/(x)-(5x)/(x+2)=(6(x+2))/(x(x+2))-(x(5x))/(x(x+2))\\\\\\=(6x+12-5x^2)/(x(x+2))=\boxed{(-5x^2+6x+12)/(x^2+2x)}`

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Additional comment

Once you realize the common denominator is x(x+2) = x²+2x, you have eliminated all but the correct answer choice.