If `(1)/(x)+(1)/(y)=(1)/(4) and (1)/(x)-(1)/(y)=(3)/(4)`, then x=

Options

A. `(1)/(4)`
B. `(1)/(2)`
C. `2`
D. `4`

Answer

To solve the given equations:

1. **Write down the equations:**
\[ \frac{1}{x} + \frac{1}{y} = \frac{1}{4} \quad \text{(Equation 1)} \]
\[ \frac{1}{x} - \frac{1}{y} = \frac{3}{4} \quad \text{(Equation 2)} \]

2. **Add the two equations:**
\[ \left(\frac{1}{x} + \frac{1}{y}\right) + \left(\frac{1}{x} - \frac{1}{y}\right) = \frac{1}{4} + \frac{3}{4} \]
This simplifies to:
\[ \frac{1}{x} + \frac{1}{y} + \frac{1}{x} - \frac{1}{y} = 1 \]
\[ 2 \cdot \frac{1}{x} = 1 \]

3. **Solve for \(\frac{1}{x}\):**
\[ \frac{2}{x} = 1 \]
Dividing both sides by 2 gives:
\[ \frac{1}{x} = \frac{1}{2} \]

4. **Take the reciprocal to find \(x\):**
\[ x = 2 \]

Thus, the value of \(x\) is \(2\).