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Mathematics
OpenStudy (anonymous):

Show all work solving the following rational equation. 3x/2+3/2x=14/x+x/1

OpenStudy (anonymous):

confused. is the last term really \(\frac{x}{1}\) ?

OpenStudy (anonymous):

Yes it is.

OpenStudy (anonymous):

then the whole thing looks like \[\frac{3x}{2}+\frac{2x}{3}=\frac{14}{x}+\frac{x}{1}\]?

OpenStudy (anonymous):

\[\frac{ 3x }{ 2 }+\frac{ 3 }{ 2 x}=\frac{ 14}{ x }+\frac{ x}{ 1 }\\ (2x)(\frac{ 3x }{ 2 }+\frac{ 3 }{ 2 x}=\frac{ 14}{ x }+\frac{ x}{ 1 })\\ 3x^2+3=28+2x^2\\ 3x^2-2x^2=28-3\\ x^2=25\\x=\pm\sqrt25\\ x=\pm5 \]

OpenStudy (anonymous):

It does satellite73.

OpenStudy (anonymous):

then louisrivera has it. multiply both sides by \(2x\) and then solve the resulting quadratic equation

OpenStudy (anonymous):

Ok thank you both for your help.

OpenStudy (anonymous):

\[\Huge\infty \]

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