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# Algebra

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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