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To solve the inequality, we first need to find a common denominator for the two fractions on the left side of the inequality:

x/(5-x) - 2/(5-x) > 1

Combine the fractions:

(x - 2)/(5-x) > 1

Now, we can multiply both sides by (5-x) to get rid of the denominator (note that since (5-x) is negative, we need to flip the inequality sign):

(5-x)(x - 2) < 5-x

Expand and simplify:

5x - x^2 - 10 + 2 < 5 - x

Rearrange the terms:

-x^2 + 6x - 7 < 0

Now, we need to find the critical points by setting the inequality to zero:

-x^2 + 6x - 7 = 0

Solve for x using the quadratic formula:

x = ( -6 ± √(6^2 - 4(-1)(-7)) ) / 2(-1) x = ( -6 ± √(36 - 28) ) / -2 x = ( -6 ± √8 ) / -2 x = ( -6 ± 2√2 ) / -2 x = 3 ± √2

So, the critical points are x = 3 + √2 and x = 3 - √2.

Now, we can test the inequality in the intervals created by the critical points:

For x < 3 - √2: Let's choose x = 0: -x^2 + 6x - 7 = -(0)^2 + 6(0) - 7 = -7 < 0

For 3 - √2 < x < 3 + √2: Let's choose x = 3: -x^2 + 6x - 7 = -(3)^2 + 6(3) - 7 = -2 < 0

For x > 3 + √2: Let's choose x = 4: -x^2 + 6x - 7 = -(4)^2 + 6(4) - 7 = 9 > 0

Therefore, the solution to the inequality is x < 3 - √2 or 3 + √2 < x.