Question

Ad(d)/(S)ubtract the rational expressions and simplify. Match with the appropriate solution. (2x)/(2)+(x+3)/(2x+2)

Answer 1

To add or subtract rational expressions, find a common denominator and combine the numerators.

Step-by-step explanation:

To add or subtract rational expressions, we need a common denominator. In this case, the common denominator is 2(2x+2). Here are the steps to add/subtract the rational expressions and simplify:

1. Multiply the first fraction by 2x+2/2x+2 to get (4x)/(4x+4).
2. Multiply the second fraction by 2/2 to get (2(x+3))/(4x+4).
3. Combine the numerators: (4x) + (2(x+3)) = 4x + 2x + 6 = 6x + 6.
4. Write the sum as a single fraction over the common denominator: (6x + 6)/(2(2x+2)).
5. Simplify the expression if possible. In this case, no further simplification is possible.