Final answer:
To solve the equation (y+3)/y = y/(y+4), we cross-multiply and simplify to eventually find y = -12/7. Then, we calculate 49y² to get 144.
Step-by-step explanation:
The question involves solving the equation (y+3)/y = y/(y+4). To find the value of 49y², we will first need to solve for y.
Firstly, we cross-multiply the given equation to eliminate the fractions:
(y + 3)(y + 4) = y²
Now, we expand and simplify the equation:
y² + 3y + 4y + 12 = y²
7y + 12 = 0
Subtract 12 from both sides:
7y = -12
Now, divide both sides by 7 to solve for y:
y = -12/7
Finally, we calculate the value of 49y² using the value of y we found:
49y² = 49(-12/7)²
49y² = 49(144/49)
49y² = 144
The value of 49y² is 144.