express 1/2 + 3/y-1 as a single fraction
well, the common denominator is 2(y-1), so that gives you
1(y-1)+3(2)
-----------------
2(y-1)
...
To express 1/2 + 3/(y-1) as a single fraction, we need to find a common denominator.
The denominator of 1/2 is 2.
The denominator of 3/(y-1) is (y-1).
To find the common denominator, we multiply the denominators together:
2 * (y-1).
Now, to adjust the numerators accordingly:
1/2 becomes (1 * (y-1))/(2 * (y-1)).
3/(y-1) remains as it is.
Combining the fractions:
(1 * (y-1))/(2 * (y-1)) + 3/(y-1) = (y-1)/(2 * (y-1)) + 3/(y-1).
Simplifying the expression:
(y-1 + 2 * 3)/(2 * (y-1)) = (y-1 + 6)/(2 * (y-1)).
Further simplification is not possible since the numerator and denominator do not have any common factors. Therefore, the expression (1/2 + 3/(y-1)) cannot be expressed as a single fraction.
To express the sum 1/2 + 3/(y-1) as a single fraction, we need to find a common denominator.
First, let's find the least common multiple (LCM) of the denominators 2 and (y-1).
The prime factorization of 2 is 2, and (y-1) is already in its simplest form.
Since there are no common factors, the LCM of 2 and (y-1) is simply their product: 2(y-1).
Now, we can rewrite 1/2 and 3/(y-1) using the common denominator of 2(y-1).
1/2 = (y-1)/(2(y-1))
3/(y-1) = 3(2)/(2(y-1))
Now we can add the fractions:
1/2 + 3/(y-1) = (y-1)/(2(y-1)) + 3(2)/(2(y-1))
Next, we simplify by combining the numerators over the common denominator:
= (y-1 + 6)/(2(y-1))
= (y + 5)/(2(y-1))
Therefore, the sum 1/2 + 3/(y-1) can be expressed as the single fraction (y + 5)/(2(y-1)).