Question

(2x+6)/((x+2)^(2))-(2)/(x+2) The expression above is equivalent to (a)/((x+2)^(2)), where a is a positive constant and x!=-2. What is the value of a ?

Answer 1

To find the value of a, we need to simplify the given expression (2x+6)/((x+2)^(2))-(2)/(x+2). By finding a common denominator and combining the numerators, we get the simplified expression 2/(x+2)^2. Therefore, the value of a is 2.

Step-by-step explanation:

To find the value of a, we need to simplify the given expression. First, let's combine the fractions by finding a common denominator of (x+2)^2. The expression becomes:

(2x+6)/((x+2)^(2)) - (2)/(x+2)

Using the common denominator, we can combine the numerators:

(2x+6) - 2(x+2)

Simplifying, we get:

2x+6 - 2x - 4

2

The final simplified expression is 2/(x+2)^2. Therefore, the value of a is 2.