`((2x + y)/(x + y) - 1) div (1 - y/(x + y))` is equal to :

Options

A. `x`
B. `y`
C. `xy`
D. `1`

Answer

To solve the expression \(\frac{(2x + y)}{(x + y)} - 1\) divided by \((1 - \frac{y}{(x + y)})\), we will follow these steps:

### Step 1: Simplify the numerator
The numerator is \(\frac{(2x + y)}{(x + y)} - 1\). To combine these terms, we need a common denominator, which is \((x + y)\).

\[ \frac{(2x + y)}{(x + y)} - 1 = \frac{(2x + y) - (x + y)}{(x + y)} = \frac{(2x + y - x - y)}{(x + y)} = \frac{x}{(x + y)} \]

### Step 2: Simplify the denominator
The denominator is \(1 - \frac{y}{(x + y)}\). Again, we will use a common denominator, which is \((x + y)\).

\[ 1 - \frac{y}{(x + y)} = \frac{(x + y) - y}{(x + y)} = \frac{x}{(x + y)} \]

### Step 3: Divide the simplified numerator by the simplified denominator
Now we have:

\[ \frac{\frac{x}{(x + y)}}{\frac{x}{(x + y)}} \]

When dividing two fractions, we multiply by the reciprocal of the denominator:

\[ \frac{x}{(x + y)} \times \frac{(x + y)}{x} \]

### Step 4: Simplify the expression
The \(x\) in the numerator and denominator cancels out, as does \((x + y)\):

\[ = 1 \]

### Final Answer
Thus, the expression \(\frac{(2x + y)}{(x + y)} - 1\) divided by \((1 - \frac{y}{(x + y)})\) is equal to \(1\).

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