Solve y=12/sqrt{3-frac{18{5}3+9}}

$$y = \frac{ 12 }{ \sqrt{ 3- \frac{ 18 }{ 5 } 3+9 } }$$

Solve for y

$$y=2\sqrt{30}\approx 10.95445115$$

Steps for Solving Linear Equation

Express \frac{18}{5}\times 3 as a single fraction.

$$y=\frac{12}{\sqrt{3-\frac{18\times 3}{5}+9}}$$

Multiply 18 and 3 to get 54.

$$y=\frac{12}{\sqrt{3-\frac{54}{5}+9}}$$

Convert 3 to fraction \frac{15}{5}.

$$y=\frac{12}{\sqrt{\frac{15}{5}-\frac{54}{5}+9}}$$

Since \frac{15}{5} and \frac{54}{5} have the same denominator, subtract them by subtracting their numerators.

$$y=\frac{12}{\sqrt{\frac{15-54}{5}+9}}$$

Subtract 54 from 15 to get -39.

$$y=\frac{12}{\sqrt{-\frac{39}{5}+9}}$$

Convert 9 to fraction \frac{45}{5}.

$$y=\frac{12}{\sqrt{-\frac{39}{5}+\frac{45}{5}}}$$

Since -\frac{39}{5} and \frac{45}{5} have the same denominator, add them by adding their numerators.

$$y=\frac{12}{\sqrt{\frac{-39+45}{5}}}$$

Add -39 and 45 to get 6.

$$y=\frac{12}{\sqrt{\frac{6}{5}}}$$

Rewrite the square root of the division \sqrt{\frac{6}{5}} as the division of square roots \frac{\sqrt{6}}{\sqrt{5}}.

$$y=\frac{12}{\frac{\sqrt{6}}{\sqrt{5}}}$$

Rationalize the denominator of \frac{\sqrt{6}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$y=\frac{12}{\frac{\sqrt{6}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}}$$

The square of \sqrt{5} is 5.

$$y=\frac{12}{\frac{\sqrt{6}\sqrt{5}}{5}}$$

To multiply \sqrt{6} and \sqrt{5}, multiply the numbers under the square root.

$$y=\frac{12}{\frac{\sqrt{30}}{5}}$$

Divide 12 by \frac{\sqrt{30}}{5} by multiplying 12 by the reciprocal of \frac{\sqrt{30}}{5}.

$$y=\frac{12\times 5}{\sqrt{30}}$$

Rationalize the denominator of \frac{12\times 5}{\sqrt{30}} by multiplying numerator and denominator by \sqrt{30}.

$$y=\frac{12\times 5\sqrt{30}}{\left(\sqrt{30}\right)^{2}}$$

The square of \sqrt{30} is 30.

$$y=\frac{12\times 5\sqrt{30}}{30}$$

Multiply 12 and 5 to get 60.

$$y=\frac{60\sqrt{30}}{30}$$

Divide 60\sqrt{30} by 30 to get 2\sqrt{30}.

$$y=2\sqrt{30}$$

Assign y

$$y≔2\sqrt{30}$$