Solve 1/2xsqrt{4x}+6xsqrt{x/9}-2x^21/x

$$\frac { 1 } { 2 } x \sqrt { 4 x } + 6 x \sqrt { \frac { x } { 9 } } - 2 x ^ { 2 } \frac { 1 } { x }$$

Factor

$$\left(3\sqrt{x}-2\right)x$$

Solution Steps

Express 2\times \frac{1}{x} as a single fraction.

$$factor(\frac{1}{2}x\sqrt{4x}+6x\sqrt{\frac{x}{9}}-\frac{2}{x}x^{2})$$

Express \frac{2}{x}x^{2} as a single fraction.

$$factor(\frac{1}{2}x\sqrt{4x}+6x\sqrt{\frac{x}{9}}-\frac{2x^{2}}{x})$$

Cancel out x in both numerator and denominator.

$$factor(\frac{1}{2}x\sqrt{4x}+6x\sqrt{\frac{x}{9}}-2x)$$

Factor out \frac{1}{2}.

$$\frac{2x\sqrt{x}+12x\times \frac{3\sqrt{x}}{9}-4x}{2}$$

Consider \sqrt{4}x^{\frac{3}{2}}+12\sqrt{\frac{1}{9}}x^{\frac{3}{2}}-4x. Factor out x.

$$x\left(2\sqrt{x}+\frac{12\sqrt{x}}{3}-4\right)$$

Rewrite the complete factored expression.

$$\frac{x\left(2\sqrt{x}+\frac{12\sqrt{x}}{3}-4\right)}{2}$$

Evaluate

$$\left(3\sqrt{x}-2\right)x$$