Question
Add the rational expressions to find the sum. 2/x + 3/x+5
Answers
GPT 3.5
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 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)).