Question

Find the two rational expressions and reduce your (4)/(x+2)+(3x^(2))/(x^(2)-4)

Answer 1

The student is looking to simplify a sum of two rational expressions by finding a common denominator and combining the terms. The simplified result will be obtained after applying these steps and reducing the expression if possible.

Step-by-step explanation:

The student is asking for help to simplify a sum of two rational expressions 4/(x+2) + 3x^2/(x^2-4). To simplify these expressions, we need to find a common denominator. In this case, the common denominator is x^2 - 4, which factors to (x+2)(x-2). Then, we can combine the two fractions.

We rewrite the first fraction so it has (x+2)(x-2) as the denominator:

1. Multiply the numerator and denominator of 4/(x+2) by (x-2) to get 4(x-2)/((x+2)(x-2)).
2. Since 3x^2/(x^2-4) is already over the common denominator, no changes are necessary for this part.
3. Add the two fractions: (4(x-2) + 3x^2)/((x+2)(x-2)).
4. Simplify the numerator by expanding and combining like terms.
5. Reduce the expression, if possible, by canceling any common factors in the numerator and denominator.

Following the above steps will lead to the simplified form of the original sum of rational expressions.