Solve 2x^2+8/x+left(8x+2/x^2right)5

$$2 { x }^{ 2 } + \frac{ 8 }{ x } + \left( 8x+ \frac{ 2 }{ { x }^{ 2 } } \right) 5$$

Evaluate

$$\frac{2\left(x^{4}+20x^{3}+4x+5\right)}{x^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 8x times \frac{x^{2}}{x^{2}}.

$$2x^{2}+\frac{8}{x}+\left(\frac{8xx^{2}}{x^{2}}+\frac{2}{x^{2}}\right)\times 5$$

Since \frac{8xx^{2}}{x^{2}} and \frac{2}{x^{2}} have the same denominator, add them by adding their numerators.

$$2x^{2}+\frac{8}{x}+\frac{8xx^{2}+2}{x^{2}}\times 5$$

Do the multiplications in 8xx^{2}+2.

$$2x^{2}+\frac{8}{x}+\frac{8x^{3}+2}{x^{2}}\times 5$$

Express \frac{8x^{3}+2}{x^{2}}\times 5 as a single fraction.

$$2x^{2}+\frac{8}{x}+\frac{\left(8x^{3}+2\right)\times 5}{x^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x^{2} times \frac{x}{x}.

$$\frac{2x^{2}x}{x}+\frac{8}{x}+\frac{\left(8x^{3}+2\right)\times 5}{x^{2}}$$

Since \frac{2x^{2}x}{x} and \frac{8}{x} have the same denominator, add them by adding their numerators.

$$\frac{2x^{2}x+8}{x}+\frac{\left(8x^{3}+2\right)\times 5}{x^{2}}$$

Do the multiplications in 2x^{2}x+8.

$$\frac{2x^{3}+8}{x}+\frac{\left(8x^{3}+2\right)\times 5}{x^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{2x^{3}+8}{x} times \frac{x}{x}.

$$\frac{\left(2x^{3}+8\right)x}{x^{2}}+\frac{\left(8x^{3}+2\right)\times 5}{x^{2}}$$

Since \frac{\left(2x^{3}+8\right)x}{x^{2}} and \frac{\left(8x^{3}+2\right)\times 5}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(2x^{3}+8\right)x+\left(8x^{3}+2\right)\times 5}{x^{2}}$$

Do the multiplications in \left(2x^{3}+8\right)x+\left(8x^{3}+2\right)\times 5.

$$\frac{2x^{4}+8x+40x^{3}+10}{x^{2}}$$

Expand

$$\frac{2\left(x^{4}+20x^{3}+4x+5\right)}{x^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 8x times \frac{x^{2}}{x^{2}}.

$$2x^{2}+\frac{8}{x}+\left(\frac{8xx^{2}}{x^{2}}+\frac{2}{x^{2}}\right)\times 5$$

Since \frac{8xx^{2}}{x^{2}} and \frac{2}{x^{2}} have the same denominator, add them by adding their numerators.

$$2x^{2}+\frac{8}{x}+\frac{8xx^{2}+2}{x^{2}}\times 5$$

Do the multiplications in 8xx^{2}+2.

$$2x^{2}+\frac{8}{x}+\frac{8x^{3}+2}{x^{2}}\times 5$$

Express \frac{8x^{3}+2}{x^{2}}\times 5 as a single fraction.

$$2x^{2}+\frac{8}{x}+\frac{\left(8x^{3}+2\right)\times 5}{x^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x^{2} times \frac{x}{x}.

$$\frac{2x^{2}x}{x}+\frac{8}{x}+\frac{\left(8x^{3}+2\right)\times 5}{x^{2}}$$

Since \frac{2x^{2}x}{x} and \frac{8}{x} have the same denominator, add them by adding their numerators.

$$\frac{2x^{2}x+8}{x}+\frac{\left(8x^{3}+2\right)\times 5}{x^{2}}$$

Do the multiplications in 2x^{2}x+8.

$$\frac{2x^{3}+8}{x}+\frac{\left(8x^{3}+2\right)\times 5}{x^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and x^{2} is x^{2}. Multiply \frac{2x^{3}+8}{x} times \frac{x}{x}.

$$\frac{\left(2x^{3}+8\right)x}{x^{2}}+\frac{\left(8x^{3}+2\right)\times 5}{x^{2}}$$

Since \frac{\left(2x^{3}+8\right)x}{x^{2}} and \frac{\left(8x^{3}+2\right)\times 5}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(2x^{3}+8\right)x+\left(8x^{3}+2\right)\times 5}{x^{2}}$$

Do the multiplications in \left(2x^{3}+8\right)x+\left(8x^{3}+2\right)\times 5.

$$\frac{2x^{4}+8x+40x^{3}+10}{x^{2}}$$