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Show that $\dfrac{2}{1-x}-\dfrac{4}{x}=3$ reduces to $3 x^{2}+3 x-4=0$.
in Mathematics by Diamond (78,454 points) | 17 views

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$ \frac{2}{1-x} - \frac{4}{x} =3$

$ 2 - \frac{4}{x} \cdot (1-x) = 3(1-x)$  (multiplying each term by (1-x))

$2 - \frac{4(1-x)}{x} = 3-3x$

$ 2x -4+4x = 3x-3x^2 $ (multplying each term by 3)

$2x-4+4x-3x+3x^2 = 0$ (taking all the terms to one side)

$ 3x^2+3x-4=0$
by Wooden (1,756 points)
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