I need help solving this rational (fractional) equation…?

Solve the equation for x

(x/(x-2))+((2x)/(4-x^2))=(5/(x+2))

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A few days ago

MsMath

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x/(x-2) + 2x/(4-x^2) = 5/(x+2)

Notice that 4 -x^2 = -(x^2 -4)

x/(x-2) + 2x/(4-x^2) = 5/(x+2)

Pull the negative from 4-x^2

x/(x-2) – 2x/(x^2 -4) = 5/(x+2)

Notice that x^2 -4 = (x+2)(x-2)

Multiply both sides by (x+2)(x-2)

x(x+2) – 2x = 5(x-2)

x^2 + 2x -2x = 5x – 10

x^2 = 5x – 10

Subtract 5x from each side and add 10 to each side

x^2 -5x + 10 = 0

This equation has no real roots. If you are interested in the imaginary roots, then use the quadratic formula.

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