If 1/x - 1/y = -29 and the value of (x + 12xy - y) / (x - 6xy - y) can be expressed as m/n, where m

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17 May 2022 Algebra

If 1/x - 1/y = -29 and the value of (x + 12xy - y) / (x - 6xy - y) can be expressed as m/n, where m and n are co prime positive integers. The value of m+n=?

OPtion

1) 52
2) 40
3) 78
4) 55
5) 68
6) 46
7) 76
8) 64
9) 56
10) None of these

Solution

1/x - 1/y = -29
(y - x)/xy = -29
y - x = -29xy or x - y = 29xy
So, (x + 12xy - y) / (x - 6xy - y) = (29xy + 12xy) / (29xy - 6xy) = 41xy/23xy = 41/23
.'. m/n = 41/23
⇒ m=41, n=23 and m+n = 41+23 = 64
Correct Option 8)

Correct Option: 8 Best Solution (0)