write as a single fraction the simplest form:
3/x + 4/x+1
If you mean (3/x) + (4/x) + 1 , then that equals 7/x + x/x = (7+x)/x
If you mean 3/x + 4/(x+1) , then form a common denominator, and you get
[3(x+1) + 4x]/[x(x+1)]
= (7x+1)/(x^2 + x)
You need to use parentheses and brackets to clarify your ambiguous typed algebraic expressions.
To simplify the expression 3/x + 4/x+1, we need to find a common denominator for both fractions. The denominators are x and x+1. To find a common denominator, we multiply the two denominators together. Thus, the common denominator is x(x+1).
To convert each fraction with the common denominator, we will multiply the numerator and denominator of the first fraction by (x+1) and the numerator and denominator of the second fraction by x.
The expression becomes:
(3 * (x+1))/(x * (x+1)) + (4 * x)/(x * (x+1))
Next, we can combine the fractions by adding their numerators together, since they have the same denominator:
(3 * (x+1) + 4 * x)/(x * (x+1))
Now we can simplify the numerator:
(3x + 3 + 4x)/(x * (x+1))
Combining like terms:
(7x + 3)/(x * (x+1))
Therefore, the simplified form of the expression 3/x + 4/x+1 is (7x + 3)/(x * (x+1)).
To write the expression (3/x) + (4/(x+1)) as a single fraction in simplest form, we need to find a common denominator for both fractions.
The denominators are x and (x+1), so the common denominator is x(x+1).
Now, we need to rewrite each fraction with the common denominator:
(3/x) * ((x+1)/(x+1)) = (3(x+1))/(x(x+1)) = (3x+3)/(x(x+1))
(4/(x+1)) * (x/x) = (4x)/(x(x+1))
Now, we can add the fractions with the common denominator:
((3x+3) + (4x))/(x(x+1)) = (7x+3)/(x(x+1))
Therefore, the expression (3/x) + (4/(x+1)) can be simplified as (7x+3)/(x(x+1)).