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(5x/x-2) - 7 = (10/x-2)

Add 7 to both sides

(5x/x-2) = (10/x-2) + 7

Multiply both sides by (x-2)

5x = 10 + 7x - 14

Simplify

5x = 7x - 4

X = 2

However this doesn't satisfy the original equation; we end up dividing by 0. This...

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(5x/x-2) - 7 = (10/x-2)

Add 7 to both sides

(5x/x-2) = (10/x-2) + 7

Multiply both sides by (x-2)

5x = 10 + 7x - 14

Simplify

5x = 7x - 4

X = 2

However this doesn't satisfy the original equation; we end up dividing by 0. This is easier to see in a graph;

Both equations have an asymptote at x=2.

Thus, the solution to this problem is not a specific value of x, because all X values are permitted except the value 2. Thus we would say that the domain is x `!=` 2, or that a vertical asymptote is located at x=2

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