Solve x+5/x^2+7x^2+7x-15

$$x+ \frac{ 5 }{ { x }^{ 2 } } +7 { x }^{ 2 } +7x-15$$

Evaluate

$$7x^{2}+8x-15+\frac{5}{x^{2}}$$

Short Solution Steps

Combine x and 7x to get 8x.

$$8x+\frac{5}{x^{2}}+7x^{2}-15$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 8x+7x^{2}-15 times \frac{x^{2}}{x^{2}}.

$$\frac{\left(8x+7x^{2}-15\right)x^{2}}{x^{2}}+\frac{5}{x^{2}}$$

Since \frac{\left(8x+7x^{2}-15\right)x^{2}}{x^{2}} and \frac{5}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(8x+7x^{2}-15\right)x^{2}+5}{x^{2}}$$

Do the multiplications in \left(8x+7x^{2}-15\right)x^{2}+5.

$$\frac{8x^{3}+7x^{4}-15x^{2}+5}{x^{2}}$$

Factor

$$\frac{7x^{4}+8x^{3}-15x^{2}+5}{x^{2}}$$