To simplify the complex fraction, we will follow these steps:
Step 1: Simplify the numerator
The numerator is y - (3y - 5)/5. To simplify it, we distribute the division by 5 to both terms inside the parentheses:
y - (3y - 5)/5 = y - (3y/5 - 5/5)
Next, we subtract the fractions with the same denominator:
y - (3y/5 - 1) = y - (3y/5 + (-1))
Step 2: Simplify the denominator
The denominator is (14/10 + 7/2y). To simplify it, we need to find a common denominator for both fractions. The least common multiple (LCM) of 10 and 2y is 10y.
Therefore, we multiply the first fraction by 2y/2y and the second fraction by 10/10:
(14/10 + 7/2y) = (14/10)(2y/2y) + (7/2y)(10/10)
Simplifying the fractions yields:
(28y/20 + 70/20y) = (28y + 70)/(20y)
Step 3: Combine the simplified numerator and denominator
Now that we have simplified the numerator and denominator, we can rewrite the fraction as:
(y - (3y/5 + (-1))) / ((28y + 70)/(20y))
To simplify further, we can flip the second fraction and multiply:
(y - (3y/5 + (-1))) * (20y/(28y + 70))
Expanding the expression, we get:
(20y(y) - 20y(3y/5 + (1))) / (28y + 70)
(20y^2 - 60y^2/5 - 20y) / (28y + 70)
Lastly, we can simplify the numerator by combining like terms:
(20y^2 - 12y^2 - 20y) / (28y + 70)
(8y^2 - 20y) / (28y + 70)
So, the simplified complex fraction is (8y^2 - 20y) / (28y + 70).