# How do you multiply # 1 / (x(x - 2))+ x /(x - 2) = 10/ x#?

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To solve the equation 1 / (x(x - 2)) + x / (x - 2) = 10 / x, we can start by finding a common denominator for the fractions on the left side of the equation. The common denominator is x(x - 2).

Multiplying the first fraction by (x - 2) / (x - 2) and the second fraction by x / x, we get:

[(1 * (x - 2)) / (x(x - 2))] + [(x * x) / (x(x - 2))] = 10 / x

Simplifying the fractions, we have:

[(x - 2) / (x^2 - 2x)] + (x^2 / (x^2 - 2x)) = 10 / x

Combining the fractions, we get:

[(x - 2) + x^2] / (x^2 - 2x) = 10 / x

Expanding the numerator, we have:

(x - 2 + x^2) / (x^2 - 2x) = 10 / x

Rearranging the equation, we get:

(x^2 + x - 2) / (x^2 - 2x) = 10 / x

Cross-multiplying, we have:

x(x^2 + x - 2) = 10(x^2 - 2x)

Expanding both sides, we get:

x^3 + x^2 - 2x = 10x^2 - 20x

Rearranging the equation, we have:

x^3 + x^2 - 10x^2 + 20x - 2x = 0

Combining like terms, we get:

x^3 - 9x^2 + 18x - 2x = 0

Simplifying further, we have:

x^3 - 9x^2 + 16x = 0

Factoring out an x, we get:

x(x^2 - 9x + 16) = 0

Factoring the quadratic expression, we have:

x(x - 1)(x - 16) = 0

Therefore, the solutions to the equation are x = 0, x = 1, and x = 16.

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