If `(4)/(x+1)=(8)/(y-2)` where `xn2-1 and yne2`, what is terms of x?

Options

A. `y=2x+1`
B. `y=2(x+2)`
C. `y=2x`
D. `y=4x+2`

Answer

To solve the equation \(\frac{4}{x+1} = \frac{8}{y-2}\) for \(y\) in terms of \(x\), we can follow these steps:

### Step 1: Write down the given equation
We start with the equation:
\[ \frac{4}{x+1} = \frac{8}{y-2} \]

### Step 2: Simplify the equation
Notice that both 4 and 8 can be simplified by taking out a common factor of 4:
\[ \frac{4}{x+1} = \frac{4 \cdot 2}{y-2} \]
This simplifies to:
\[ \frac{1}{x+1} = \frac{2}{y-2} \]

### Step 3: Cross multiply
Now, we will cross multiply to eliminate the fractions:
\[ 1 \cdot (y - 2) = 2 \cdot (x + 1) \]
This simplifies to:
\[ y - 2 = 2(x + 1) \]

### Step 4: Expand the equation
Now, we will expand the right-hand side:
\[ y - 2 = 2x + 2 \]

### Step 5: Solve for \(y\)
Next, we will isolate \(y\) by adding 2 to both sides:
\[ y = 2x + 2 + 2 \]
This simplifies to:
\[ y = 2x + 4 \]

### Step 6: Factor the equation (optional)
We can also factor out the 2:
\[ y = 2(x + 2) \]

### Final Answer
Thus, the value of \(y\) in terms of \(x\) is:
\[ y = 2x + 4 \]

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