Question 161508
{{{1/x - (x-4)/x = 1/x + 3/20}}} Start with the given equation.



{{{(20x)(1/cross(x)) - (20x)((x-4)/cross(x)) = (20x)(1/cross(x)) + (20x)(3/cross(20))}}} Multiply <b>every</b> term by the LCD {{{20x}}} to clear the fractions.




{{{20 - 20(x-4) = 20 + 3x}}} Multiply and simplify



{{{20-20x+80=20+3x}}} Distribute.



{{{-20x+100=20+3x}}} Combine like terms on the left side.



{{{-20x=20+3x-100}}} Subtract {{{100}}} from both sides.



{{{-20x-3x=20-100}}} Subtract {{{3x}}} from both sides.



{{{-23x=20-100}}} Combine like terms on the left side.



{{{-23x=-80}}} Combine like terms on the right side.



{{{x=(-80)/(-23)}}} Divide both sides by {{{-23}}} to isolate {{{x}}}.



{{{x=80/23}}} Reduce.



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Answer:


So the answer is {{{x=80/23}}} which approximates to {{{x=3.478}}}.