Question

Subtract the rational expressions:

x/x+1 - 2/x
a. x-2/x+1
b. 2-x/x+1
c. x+2/x
d. x²-2/x(x+1)

Answer 1

To subtract the expressions x/(x+1) - 2/x, we find a common denominator which is x(x+1), rewrite the expressions accordingly, and subtract them to get the answer x^2 - 2 / x(x + 1).

Step-by-step explanation:

Subtracting Rational Expressions

To subtract the rational expressions x/(x+1) - 2/x, we first need to find a common denominator. The common denominator between x+1 and x is x(x+1). We then rewrite each fraction with this common denominator:

(x * x) / (x(x+1)) - (2 * (x+1)) / (x(x+1))

Now that they have the same denominator, we can subtract the numerators:

(x^2 - 2(x + 1)) / (x(x+1))

Next, we expand the numerator and combine like terms:

(x^2 - 2x - 2) / (x(x+1))

This simplifies to:

x2 - 2x - 2 / x(x + 1)

Therefore, the correct answer is d. x2 - 2 / x(x + 1).