Solve (9x^6-12x^5+40x^3+52x^2-48x+16)div{x}^2+2

$$(9 { x }^{ 6 } -12 { x }^{ 5 } +40 { x }^{ 3 } +52 { x }^{ 2 } -48x+16) \div { x }^{ 2 } +2$$

Evaluate

$$9x^{4}-12x^{3}+40x+54-\frac{48}{x}+\frac{16}{x^{2}}$$

Short Solution Steps

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

$$\frac{9x^{6}-12x^{5}+40x^{3}+52x^{2}-48x+16}{x^{2}}+\frac{2x^{2}}{x^{2}}$$

Since \frac{9x^{6}-12x^{5}+40x^{3}+52x^{2}-48x+16}{x^{2}} and \frac{2x^{2}}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{9x^{6}-12x^{5}+40x^{3}+52x^{2}-48x+16+2x^{2}}{x^{2}}$$

Combine like terms in 9x^{6}-12x^{5}+40x^{3}+52x^{2}-48x+16+2x^{2}.

$$\frac{-48x+9x^{6}-12x^{5}+40x^{3}+54x^{2}+16}{x^{2}}$$

Expand

$$9x^{4}-12x^{3}+40x+54-\frac{48}{x}+\frac{16}{x^{2}}$$

Short Solution Steps

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

$$\frac{9x^{6}-12x^{5}+40x^{3}+52x^{2}-48x+16}{x^{2}}+\frac{2x^{2}}{x^{2}}$$

Since \frac{9x^{6}-12x^{5}+40x^{3}+52x^{2}-48x+16}{x^{2}} and \frac{2x^{2}}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{9x^{6}-12x^{5}+40x^{3}+52x^{2}-48x+16+2x^{2}}{x^{2}}$$

Combine like terms in 9x^{6}-12x^{5}+40x^{3}+52x^{2}-48x+16+2x^{2}.

$$\frac{-48x+9x^{6}-12x^{5}+40x^{3}+54x^{2}+16}{x^{2}}$$