use any method to simplify the complex fraction.
y-(3y-5)/5/(14/10 + 7/2y)
the fraction simplifies to ___.
a/b/c = a/(bc)
so, we have
(3y-5)/5/(14/10 + 7/2 y)
= (3y-5)/(5*7(1/5 + 1/2 y))
= (3y-5)/(35*(2+5y)/10)
= 2(3y-5)/(7(2+5y))
Now subtract that from y and you have
7y(2+5y) - 2(3y-5)
-----------------------
7(5y+2)
(35y^2+8y+10)/(35y+14)
To simplify the given complex fraction, we will follow these steps:
Step 1: Simplify the numerator of the complex fraction.
- Distribute the denominator 5 to both terms in the numerator:
y - (3y - 5)/5 = y - (3y/5) + 1 = y - (3/5)y + 1
Step 2: Simplify the denominator of the complex fraction.
To simplify the denominator, we need to find the least common denominator (LCD) between 10 and 2y. The LCD is 10y.
14/10 + 7/2y = (14y + 35)/10y
Step 3: Rewrite the complex fraction with the simplified numerator and denominator.
y - (3/5)y + 1 / (14y + 35)/10y
Step 4: Simplify the complex fraction by multiplying the numerator by the reciprocal of the denominator.
(y - (3/5)y + 1) * (10y / (14y + 35))
Step 5: Simplify the numerator and denominator of the complex fraction.
Numerator:
y - (3/5)y + 1 = (5y - 3y + 5)/5 = (2y + 5)/5
Denominator:
(14y + 35)/10y = (7y + 35)/(5y) = 7(y + 5)/5y
Step 6: Rewrite the complex fraction with the simplified numerator and denominator.
(2y + 5)/5 / 7(y + 5)/5y
Step 7: Simplify the complex fraction by multiplying the numerator by the reciprocal of the denominator.
(2y + 5)/5 * (5y/7(y + 5))
Step 8: Simplify the numerator and denominator of the complex fraction.
Numerator:
(2y + 5)*5y = 10y^2 + 25y
Denominator:
7(y + 5)
Step 9: Rewrite the complex fraction with the simplified numerator and denominator.
(10y^2 + 25y)/7(y + 5)
Therefore, the given complex fraction simplifies to (10y^2 + 25y)/7(y + 5).
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).