Question

Simplify 1/x+2 + 1/x+3 and give your answer in form of f(x)/g(x).

Answer 1

To simplify the expression 1/(x+2) + 1/(x+3), find a common denominator and combine like terms in the numerator. The simplified expression is (2x+5)/((x+2)(x+3)).

Step-by-step explanation:

To simplify the expression 1/(x+2) + 1/(x+3), we need to find a common denominator. The common denominator in this case is (x+2)(x+3). So, we can rewrite the expression as follows:

(1*(x+3) + 1*(x+2))/((x+2)(x+3))

Combining like terms in the numerator, we get:

((x+3) + (x+2))/((x+2)(x+3))

Expanding the numerator, we get:

(2x + 5)/((x+2)(x+3))

Therefore, the simplified expression is f(x) = 2x + 5 and g(x) = (x+2)(x+3). The answer can be written as f(x)/g(x) = (2x+5)/((x+2)(x+3)).