Add the rational expressions to find the sum. 5/x+2 + 6/x-3
To add these rational expressions, we need to find a common denominator. In this case, the common denominator is (x + 2)(x - 3).
Now, we can rewrite each expression with the common denominator:
(5/x + 2) = (5(x - 3))/((x + 2)(x - 3)) = (5x - 15)/((x + 2)(x - 3))
(6/x - 3) = (6(x + 2))/((x + 2)(x - 3)) = (6x + 12)/((x + 2)(x - 3))
Now, we can add the fractions:
(5x - 15)/((x + 2)(x - 3)) + (6x + 12)/((x + 2)(x - 3)) = (5x + 6x) + (-15 + 12)/((x + 2)(x - 3))
Simplifying:
11x - 3/((x + 2)(x - 3))
Therefore, the sum of the rational expressions 5/x + 2 and 6/x - 3 is (11x - 3)/((x + 2)(x - 3)).
To add rational expressions, we need to find a common denominator first.
The denominators in this case are x+2 and x-3. To find a common denominator, we multiply the denominators together:
(x+2) * (x-3)
Next, we need to rewrite each fraction with the common denominator:
5/(x+2) = 5 * (x-3) / [(x+2) * (x-3)] = (5x -15) / [(x+2) * (x-3)]
6/(x-3) = 6 * (x+2) / [(x+2) * (x-3)] = (6x + 12) / [(x+2) * (x-3)]
Now that both fractions have the same denominator, we can add them together:
(5x - 15) / [(x+2) * (x-3)] + (6x + 12) / [(x+2) * (x-3)]
To add the fractions, we add the numerators and keep the denominators the same:
[(5x - 15) + (6x + 12)] / [(x+2) * (x-3)]
Simplifying the numerator:
(5x - 15 + 6x + 12) / [(x+2) * (x-3)] = (11x - 3) / [(x+2) * (x-3)]
So, the sum of the rational expressions 5/x+2 + 6/x-3 is (11x - 3) / [(x+2) * (x-3)].
To add rational expressions, you need to have a common denominator. In this case, the denominators are x+2 and x-3. To find the common denominator, you need to multiply the two denominators together.
The common denominator for (x+2) and (x-3) is (x+2)(x-3). To add the rational expressions, you need to rewrite each fraction with the common denominator.
The first fraction, 5/(x+2), can be rewritten as (5(x-3))/[(x+2)(x-3)].
The second fraction, 6/(x-3), can be rewritten as (6(x+2))/[(x+2)(x-3)].
Now that both fractions have a common denominator, you can add them directly:
(5(x-3) + 6(x+2))/[(x+2)(x-3)]
Simplifying the numerator gives:
(5x-15 + 6x+12)/[(x+2)(x-3)]
Combine like terms:
(11x - 3)/[(x+2)(x-3)]
So the sum of the rational expressions 5/x+2 and 6/x-3 is (11x - 3)/[(x+2)(x-3)].