Question 195571


{{{2/(x+3)+1/x=(4)/(3x)}}} Start with the given equation.



{{{3x*cross((x+3))(2/cross((x+3)))+3cross(x)(x+3)(1/cross(x))=cross(3x)(x+3)((4)/cross(3x))}}} Multiply <font size="4"><b>every</b></font> term on both sides by the LCD {{{3x(x+3)}}}. Doing this will eliminate all of the fractions.



{{{3x(2)+3(x+3)(1)=4(x+3)}}} Cancel out and simplify



{{{6x+3(x+3)=4(x+3)}}} Multiply



{{{6x+3x+9=4x+12}}} Distribute.



{{{9x+9=4x+12}}} Combine like terms on the left side.



{{{9x=4x+12-9}}} Subtract {{{9}}} from both sides.



{{{9x-4x=12-9}}} Subtract {{{4x}}} from both sides.



{{{5x=12-9}}} Combine like terms on the left side.



{{{5x=3}}} Combine like terms on the right side.



{{{x=(3)/(5)}}} Divide both sides by {{{5}}} to isolate {{{x}}}.



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Answer:


So the answer is {{{x=3/5}}} which in decimal form is {{{x=0.6}}}.