Question

1/x - 1/x-2 = 3 solve for x

Answer 1

$\bf\purple{\underline{\boxed{Question}}}$

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$\small\tt{{\frac{1}{x}}\:-\:{\frac{1}{x-2}}\:=\:3\:\:\:solve\:for\:x}$

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$\bf\purple{\underline{\boxed{Solution}}}$

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✏

$\small\tt{{\frac{1}{x}}\:-\:{\frac{1}{x-2}}\:=\:3\:}$

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$\small\text{Lcm of 1/x and 1/x-2 will be x(x-2)}$

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$\small\text{so,}$

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$\small\tt{{\frac{x-2-x}{x(x-2)}}\:=\:3\:}$

$\small\tt{x-2-x\:=\:x(x-2) \times 3\:}$

$\small\tt{-2\:=\:(x^{2}-2x)\times 3\:}$

$\small\tt{-2\:=\:(3x^{2}-6x)}$

$\small\tt{0\:=\:3x^{2}-6x+2}$

$\small\tt{3x^{2}-6x+2\:=\:0}$

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$\small\text{Now factorise it for finding the value of x}$

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$\small\tt{3x^{2}-6x+2\:=\:0}$

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$\small\tt{where\:\:,}$

$\small\tt{a\:=\:3}$

$\small\tt{b\:=\:6}$

$\small\tt{c\:=\:2}$

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$\small\tt{using\: formula}\\{\small\tt{D\:=\:b^{2}-4ac}}$

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$\small\tt{\:=\:6^{2}-4\times3\times2}$

$\small\tt{\:=\:36\:-\:24}$

$\small\tt{D\:=\: 12}$

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✒$\rm{\ 3x^{2}-6x+2}$

$\rm{x\:=\:\frac{-b±\sqrt{ \ b^{2}-4ac}}{2a}}$

$\rm{x\:=\:\frac{-(-6)±\sqrt{ 12}}{2 \times 3}}$

$\rm{x\:=\:\frac{+6±\sqrt{ 12}}{6}}$

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$\small\text{There are 2 possible values}$

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$\small\text{1) Postive}$

$\rm{x\:=\:\frac{6+\sqrt{ 12}}{6}}$

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$\small\text{2) Negetive\:}$

$\rm{x\:=\:\frac{6-\sqrt{ 12}}{6}}$

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$\bf\purple{\underline{\boxed{Thanks}}}$