Solve frac{4x^{9}+2x^{6}y^{2}+4x^{3}+2y^2}{8x^6+4x^3y^2}

$$\frac { 4 x ^ { 9 } + 2 x ^ { 6 } y ^ { 2 } + 4 x ^ { 3 } + 2 y ^ { 2 } } { 8 x ^ { 6 } + 4 x ^ { 3 } y ^ { 2 } }$$

Evaluate

$$\frac{x^{6}+1}{2x^{3}}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{2\left(x^{2}+1\right)\left(2x^{3}+y^{2}\right)\left(x^{4}-x^{2}+1\right)}{4x^{3}\left(2x^{3}+y^{2}\right)}$$

Cancel out 2\left(2x^{3}+y^{2}\right) in both numerator and denominator.

$$\frac{\left(x^{2}+1\right)\left(x^{4}-x^{2}+1\right)}{2x^{3}}$$

Expand the expression.

$$\frac{x^{6}+1}{2x^{3}}$$

Expand

$$\frac{x^{6}+1}{2x^{3}}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{2\left(x^{2}+1\right)\left(2x^{3}+y^{2}\right)\left(x^{4}-x^{2}+1\right)}{4x^{3}\left(2x^{3}+y^{2}\right)}$$

Cancel out 2\left(2x^{3}+y^{2}\right) in both numerator and denominator.

$$\frac{\left(x^{2}+1\right)\left(x^{4}-x^{2}+1\right)}{2x^{3}}$$

Expand the expression.

$$\frac{x^{6}+1}{2x^{3}}$$