To solve this equation, we can first find a common denominator for all the fractions on both sides. The least common denominator here is (x-5)(x-7)(x-1)(x-3).
Multiplying each term by this common denominator, we get:
(x-7)(x-1)(x-3) - (x-5)(x-1)(x-3) = (x-5)(x-7)(x-1) - (x-5)(x-7)(x-3)
Expanding each term, we get:
(x^3 - 8x^2 + 15x - 21) - (x^3 - 8x^2 + 16x - 15) = (x^3 - 13x^2 + 42x - 35) - (x^3 - 8x^2 - 12x + 105)
Simplifying both sides, we get:
-6x + 6 = 32x - 140
Combining like terms:
32x + 6x = 140 + 638x = 146x = 146/38x = 73/19
Therefore, the solution to the equation 1/(x-5) - 1/(x-7) = 1/(x-1) - 1/(x-3) is x = 73/19.
To solve this equation, we can first find a common denominator for all the fractions on both sides. The least common denominator here is (x-5)(x-7)(x-1)(x-3).
Multiplying each term by this common denominator, we get:
(x-7)(x-1)(x-3) - (x-5)(x-1)(x-3) = (x-5)(x-7)(x-1) - (x-5)(x-7)(x-3)
Expanding each term, we get:
(x^3 - 8x^2 + 15x - 21) - (x^3 - 8x^2 + 16x - 15) = (x^3 - 13x^2 + 42x - 35) - (x^3 - 8x^2 - 12x + 105)
Simplifying both sides, we get:
-6x + 6 = 32x - 140
Combining like terms:
32x + 6x = 140 + 6
38x = 146
x = 146/38
x = 73/19
Therefore, the solution to the equation 1/(x-5) - 1/(x-7) = 1/(x-1) - 1/(x-3) is x = 73/19.