Solve the following simultaneous equations: 10/(x + y) + 2/(x - y) = 4 ; 15/(x + y) - 5/(x - y) = -2

Answer: \((x, y) = (3, 2)\)

Put \(\frac{1}{x+y} = m\) and \(\frac{1}{x-y} = n\).

The equations become \(10m + 2n = 4\) ... (III) and \(15m - 5n = -2\) ... (IV).

Multiply (III) by 5: \(50m + 10n = 20\)
Multiply (IV) by 2: \(30m - 10n = -4\)

Add the equations to eliminate \(n\):\[80m = 16\]\[m = \frac{1}{5}\]

Substitute \(m = \frac{1}{5}\) in (III): \(2n = 4 - 2 = 2\), so \(n = 1\).

Check in (IV): \(15(\frac{1}{5}) + (-5)(1) = -2\), which is true.

So \(x + y = \frac{1}{m} = 5\) ... (V) and \(x - y = \frac{1}{n} = 1\) ... (VI). Adding: \(2x = 6\), \(x = 3\); then \(y = 5 - 3 = 2\).