Solve frac{sqrt{42}x^2-sqrt{6^3}x}{7x^2-6}

$$\frac{ \sqrt{ 42 } { x }^{ 2 } - \sqrt{ { 6 }^{ 3 } } x }{ 7 { x }^{ 2 } -6 }$$

Evaluate

$$\frac{x\left(\sqrt{42}x-6\sqrt{6}\right)}{7x^{2}-6}$$

Short Solution Steps

Calculate 6 to the power of 3 and get 216.

$$\frac{\sqrt{42}x^{2}-\sqrt{216}x}{7x^{2}-6}$$

Factor 216=6^{2}\times 6. Rewrite the square root of the product \sqrt{6^{2}\times 6} as the product of square roots \sqrt{6^{2}}\sqrt{6}. Take the square root of 6^{2}.

$$\frac{\sqrt{42}x^{2}-6\sqrt{6}x}{7x^{2}-6}$$

Factor

$$\frac{x\left(\sqrt{42}x-6\sqrt{6}\right)}{7x^{2}-6}$$