$\frac{ {\left( 7-3x \right)}^{\frac{ 1 }{ 2 }}+\frac{ 3x \times {\left( 7-3x \right)}^{-\frac{ 1 }{ 2 }} }{ 2 } }{ 7-3x }$
If a negative exponent is in the numerator, move the expression to the denominator and make the exponent positive$\frac{ {\left( 7-3x \right)}^{\frac{ 1 }{ 2 }}+\frac{ 3x }{ 2{\left( 7-3x \right)}^{\frac{ 1 }{ 2 }} } }{ 7-3x }$
Write all numerators above the common denominator$\frac{ \frac{ 2\left( 7-3x \right)+3x }{ 2{\left( 7-3x \right)}^{\frac{ 1 }{ 2 }} } }{ 7-3x }$
Distribute $2$ through the parentheses$\frac{ \frac{ 14-6x+3x }{ 2{\left( 7-3x \right)}^{\frac{ 1 }{ 2 }} } }{ 7-3x }$
Collect like terms$\frac{ \frac{ 14-3x }{ 2{\left( 7-3x \right)}^{\frac{ 1 }{ 2 }} } }{ 7-3x }$
Simplify the complex fraction$\frac{ 14-3x }{ 2{\left( 7-3x \right)}^{\frac{ 1 }{ 2 }} \times \left( 7-3x \right) }$
Use ${a}^{\frac{ m }{ n }}=\sqrt[n]{{a}^{m}}$ to transform the expression$\frac{ 14-3x }{ 2\sqrt{ 7-3x }\left( 7-3x \right) }$