If `(4)/(y)+4=(20)/(y)+20`, then what is the value of `(4)/(y)+4` ?

Options

A. `-1`
B. 0
C. 1
D. 4

Explanation

To solve the equation \( \frac{4}{y} + 4 = \frac{20}{y} + 20 \), we will follow these steps:

### Step 1: Rearrange the equation
Start by moving all terms involving \( y \) to one side and constant terms to the other side:
\[ \frac{4}{y} - \frac{20}{y} = 20 - 4 \]

### Step 2: Combine the fractions
Since both terms on the left side have a common denominator \( y \), we can combine them:
\[ \frac{4 - 20}{y} = 16 \]
This simplifies to:
\[ \frac{-16}{y} = 16 \]

### Step 3: Cross-multiply
To eliminate the fraction, we can cross-multiply:
\[ -16 = 16y \]

### Step 4: Solve for \( y \)
Now, divide both sides by 16:
\[ y = \frac{-16}{16} = -1 \]

### Step 5: Substitute \( y \) back into the expression
Now that we have \( y = -1 \), we substitute it back into the expression \( \frac{4}{y} + 4 \):
\[ \frac{4}{-1} + 4 = -4 + 4 \]

### Step 6: Simplify the expression
This simplifies to:
\[ 0 \]

Thus, the value of \( \frac{4}{y} + 4 \) is \( 0 \).

### Final Answer:
The value of \( \frac{4}{y} + 4 \) is \( 0 \).

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