Solve 6x-1+1/3x/sqrt{200-19}

$$\frac { 6 x - 1 + \frac { 1 } { 3 } x } { \sqrt { 200 - 19 } }$$

Evaluate

$$\frac{\sqrt{181}\left(19x-3\right)}{543}$$

Solution Steps

Combine 6x and \frac{1}{3}x to get \frac{19}{3}x.

$$\frac{\frac{19}{3}x-1}{\sqrt{200-19}}$$

Subtract 19 from 200 to get 181.

$$\frac{\frac{19}{3}x-1}{\sqrt{181}}$$

Rationalize the denominator of \frac{\frac{19}{3}x-1}{\sqrt{181}} by multiplying numerator and denominator by \sqrt{181}.

$$\frac{\left(\frac{19}{3}x-1\right)\sqrt{181}}{\left(\sqrt{181}\right)^{2}}$$

The square of \sqrt{181} is 181.

$$\frac{\left(\frac{19}{3}x-1\right)\sqrt{181}}{181}$$

Use the distributive property to multiply \frac{19}{3}x-1 by \sqrt{181}.

$$\frac{\frac{19}{3}x\sqrt{181}-\sqrt{181}}{181}$$

Factor

$$\frac{\sqrt{181}\left(19x-3\right)}{543}$$

Solution Steps

Combine 6x and \frac{1}{3}x to get \frac{19}{3}x.

$$factor(\frac{\frac{19}{3}x-1}{\sqrt{200-19}})$$

Subtract 19 from 200 to get 181.

$$factor(\frac{\frac{19}{3}x-1}{\sqrt{181}})$$

Rationalize the denominator of \frac{\frac{19}{3}x-1}{\sqrt{181}} by multiplying numerator and denominator by \sqrt{181}.

$$factor(\frac{\left(\frac{19}{3}x-1\right)\sqrt{181}}{\left(\sqrt{181}\right)^{2}})$$

The square of \sqrt{181} is 181.

$$factor(\frac{\left(\frac{19}{3}x-1\right)\sqrt{181}}{181})$$

Use the distributive property to multiply \frac{19}{3}x-1 by \sqrt{181}.

$$factor(\frac{\frac{19}{3}x\sqrt{181}-\sqrt{181}}{181})$$

Consider \frac{19}{3}x\times 181^{\frac{1}{2}}-181^{\frac{1}{2}}. Factor out \frac{1}{3}.

$$\frac{19x\sqrt{181}-3\sqrt{181}}{3}$$

Consider 19x\sqrt{181}-3\sqrt{181}. Factor out \sqrt{181}.

$$\sqrt{181}\left(19x-3\right)$$

Rewrite the complete factored expression. Simplify.

$$\frac{\left(19x-3\right)\sqrt{181}}{543}$$