Solve 3/2sqrt{2}+6/x^7-10x

$$\frac{ 3 }{ 2 \sqrt{ 2 } } + \frac{ 6 }{ { x }^{ 7 } } -10x$$

Evaluate

$$-10x+\frac{3\sqrt{2}}{4}+\frac{6}{x^{7}}$$

Short Solution Steps

Rationalize the denominator of \frac{3}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{3\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}+\frac{6}{x^{7}}-10x$$

The square of \sqrt{2} is 2.

$$\frac{3\sqrt{2}}{2\times 2}+\frac{6}{x^{7}}-10x$$

Multiply 2 and 2 to get 4.

$$\frac{3\sqrt{2}}{4}+\frac{6}{x^{7}}-10x$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and x^{7} is 4x^{7}. Multiply \frac{3\sqrt{2}}{4} times \frac{x^{7}}{x^{7}}. Multiply \frac{6}{x^{7}} times \frac{4}{4}.

$$\frac{3\sqrt{2}x^{7}}{4x^{7}}+\frac{6\times 4}{4x^{7}}-10x$$

Since \frac{3\sqrt{2}x^{7}}{4x^{7}} and \frac{6\times 4}{4x^{7}} have the same denominator, add them by adding their numerators.

$$\frac{3\sqrt{2}x^{7}+6\times 4}{4x^{7}}-10x$$

Do the multiplications in 3\sqrt{2}x^{7}+6\times 4.

$$\frac{3\sqrt{2}x^{7}+24}{4x^{7}}-10x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -10x times \frac{4x^{7}}{4x^{7}}.

$$\frac{3\sqrt{2}x^{7}+24}{4x^{7}}+\frac{-10x\times 4x^{7}}{4x^{7}}$$

Since \frac{3\sqrt{2}x^{7}+24}{4x^{7}} and \frac{-10x\times 4x^{7}}{4x^{7}} have the same denominator, add them by adding their numerators.

$$\frac{3\sqrt{2}x^{7}+24-10x\times 4x^{7}}{4x^{7}}$$

Do the multiplications in 3\sqrt{2}x^{7}+24-10x\times 4x^{7}.

$$\frac{3\sqrt{2}x^{7}+24-40x^{8}}{4x^{7}}$$

Factor

$$\frac{-40x^{8}+3\sqrt{2}x^{7}+24}{4x^{7}}$$