Question

In this activity, you will combine these rational expressions by addition, subtraction, multiplication, and division: x/(x+1) + 2/x

a) 3x/(x²+x)
b) (3x+2)/(x²+x)
c) (3x²+2)/(x²+x)
d) (3x²+x+2)/(x²+x)

Answer 1

The correct combined expression of x/(x+1) + 2/x by finding a common denominator is (x² + 2x)/(x²+x), which is not listed in the options (a) to (d).

Step-by-step explanation:

When dealing with the addition of rational expressions, such as x/(x+1) + 2/x, finding a common denominator is essential. To add these two fractions, their denominators must be the same. Here, we multiply x by x and 2 by (x+1), creating a common denominator of x(x+1) or x² + x. The resulting expression is (x² + 2x)/(x²+x). This differs from the options (a) to (d). The correct process of adding fractions with different denominators involves creating a common denominator through multiplication and then adding the numerators, as outlined in the information provided.