Question

20/x-1/3=20/x+2
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Answer 1

$\frac{20}{x}-\frac{1}{3}=\frac{20}{x+2}\\\frac{20}{x}-\frac{1}{3}-\frac{20}{x+2}=0\\\frac{60(x+2)-x(x+2)-60x}{3x(x+2)}=0\\\frac{60x+120-x^2-2x-60x}{3x(x-2)}=0\\\frac{120-x^2-2x}{3x(x-2)}=0\\120-x^2-2x=0\\-x^2-2x+120=0 \: \: \: \: | \cdot (-1)\\x^2+2x-120=0\\D = 2^2 - 4 \cdot 1 \cdot (-120)=4+480=484\\\sqrt{D}=\sqrt{484}=22\\x_1=\frac{-2+22}{2}=\frac{20}{2}=10\\x_2=\frac{-2-22}{2}=\frac{-24}{2}=-12$