Formula Used: x2–y2 = (x – y)(x + y) Calculation: x/y – y/x ⇒ (x2–y2)∕xy ⇒ (x – y)(x + y)/xy ---- equation (1) x – y = (√2+
1
√2
)–(√2–
1
√2
) ⇒ √2+
1
√2
−√2+
1
√2
⇒
2
√2
⇒ √2 x + y = (√2+
1
√2
)+(√2–
1
√2
) ⇒ √2+
1
√2
+√2–
1
√2
⇒ 2√2 xy = (√2+
1
√2
)(√2–
1
√2
) ⇒ (√2)2–(
1
√2
)2 ⇒ 2 – 1/2 ⇒ 3/2 put the value of (x – y), (x + y), and xy in equation (1) ⇒ (x – y)(x + y)/xy ⇒ (√2 × 2√2)/(3/2) ⇒ (4 × 2)/3 ⇒ 8/3 ∴ The value of x/y – y/x is 8/3.