Add the rational expressions to find the sum. 2/x + 3/x+5
The sum of the rational expressions 2/x and 3/(x+5) can be found by first finding a common denominator. The common denominator in this case is (x)(x+5).
To add the rational expressions, we need to have the same denominator for both. So, we multiply the first rational expression by (x+5)/(x+5) and the second rational expression by (x)/(x), as follows:
(2/x) * ((x+5)/(x+5)) + (3/(x+5)) * (x/x)
= (2(x+5))/(x(x+5)) + 3x/(x(x+5))
Now that the denominators are the same, we can add the numerators:
(2(x+5) + 3x)/(x(x+5))
= (2x + 10 + 3x)/(x(x+5))
= (5x + 10)/(x(x+5))
Therefore, the sum of the rational expressions 2/x and 3/(x+5) is (5x + 10)/(x(x+5)).
To add rational expressions, we need to find a common denominator. In this case, the denominators are x and x+5.
To find the common denominator, we multiply the denominators together: x * (x+5).
Now, we need to rewrite each fraction with the common denominator:
2/x = (2 * (x+5)) / (x * (x+5))
3/(x+5) = (3 * x) / (x * (x+5))
Now, we can add the fractions:
(2 * (x+5)) / (x * (x+5)) + (3 * x) / (x * (x+5))
Next, we can combine the fractions:
(2 * (x+5) + 3 * x) / (x * (x+5))
Expanding the numerators:
(2x + 10 + 3x) / (x * (x+5))
Combine like terms:
(5x + 10) / (x * (x+5))
Therefore, the sum of the rational expressions 2/x and 3/(x+5) is (5x + 10) / (x * (x+5)).
To add rational expressions, we need to have a common denominator. In this case, the denominators are x and x + 5.
To find the common denominator, we need to take the product of the denominators. Therefore, the common denominator is (x)(x + 5).
Now, we can rewrite the rational expressions using the common denominator:
2/x = (2(x + 5))/(x(x + 5))
3/(x + 5) = (3x)/(x(x + 5))
Now that we have a common denominator, we can add the rational expressions:
(2(x + 5))/(x(x + 5)) + (3x)/(x(x + 5))
To combine the numerators, we need to find a common term, which is (x + 5). We can do this by multiplying the first term by x and the second term by (x + 5):
(2(x + 5))/(x(x + 5)) + (3x)/(x(x + 5))
= (2x + 10)/(x(x + 5)) + (3x)/(x(x + 5))
Now that we have the same denominator, we can add the numerators:
= (2x + 10 + 3x)/(x(x + 5))
= (5x + 10)/(x(x + 5))
Therefore, the sum of 2/x and 3/(x + 5) is (5x + 10)/(x(x + 5)).