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The equation 2x - 3/(x - 2) = 4- 3/(x - 2) has how many roots?

 Aug 11, 2021
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multiply by x - 2 ==> \(2x(x-2) - 3 = 4(x - 2) - 3\)

add 3 to both sides ==> \(2x(x-2) = 4(x-2)\)

simplify ==> \(2x^2 - 4x = 4x - 8\)

simplify again ==> \(2x^2 - 8x - 8 = 0 ===> x^2 - 4x - 4 = 0\)

use quadratic formula ==> \(x = {4 \pm \sqrt{(-4)^2-4*1*-4} \over 2} \)

so \(2 \) solutions

 Aug 11, 2021
edited by Guest  Aug 11, 2021

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