Solve frac{3x^{4}-9x^{2}y^2}{3x^3y}-4x^3-8x/2x^2y

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

Evaluate

$$\frac{4-3y^{2}-x^{2}}{xy}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3x^{4}-9x^{2}y^{2}}{3x^{3}y}.

$$\frac{3x^{2}\left(x^{2}-3y^{2}\right)}{3yx^{3}}-\frac{4x^{3}-8x}{2x^{2}y}$$

Cancel out 3x^{2} in both numerator and denominator.

$$\frac{x^{2}-3y^{2}}{xy}-\frac{4x^{3}-8x}{2x^{2}y}$$

Factor the expressions that are not already factored in \frac{4x^{3}-8x}{2x^{2}y}.

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

Cancel out 2x in both numerator and denominator.

$$\frac{x^{2}-3y^{2}}{xy}-\frac{2\left(x^{2}-2\right)}{xy}$$

Since \frac{x^{2}-3y^{2}}{xy} and \frac{2\left(x^{2}-2\right)}{xy} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{2}-3y^{2}-2\left(x^{2}-2\right)}{xy}$$

Do the multiplications in x^{2}-3y^{2}-2\left(x^{2}-2\right).

$$\frac{x^{2}-3y^{2}-2x^{2}+4}{xy}$$

Combine like terms in x^{2}-3y^{2}-2x^{2}+4.

$$\frac{-x^{2}-3y^{2}+4}{xy}$$

Expand

$$\frac{4-3y^{2}-x^{2}}{xy}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3x^{4}-9x^{2}y^{2}}{3x^{3}y}.

$$\frac{3x^{2}\left(x^{2}-3y^{2}\right)}{3yx^{3}}-\frac{4x^{3}-8x}{2x^{2}y}$$

Cancel out 3x^{2} in both numerator and denominator.

$$\frac{x^{2}-3y^{2}}{xy}-\frac{4x^{3}-8x}{2x^{2}y}$$

Factor the expressions that are not already factored in \frac{4x^{3}-8x}{2x^{2}y}.

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

Cancel out 2x in both numerator and denominator.

$$\frac{x^{2}-3y^{2}}{xy}-\frac{2\left(x^{2}-2\right)}{xy}$$

Since \frac{x^{2}-3y^{2}}{xy} and \frac{2\left(x^{2}-2\right)}{xy} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{2}-3y^{2}-2\left(x^{2}-2\right)}{xy}$$

Do the multiplications in x^{2}-3y^{2}-2\left(x^{2}-2\right).

$$\frac{x^{2}-3y^{2}-2x^{2}+4}{xy}$$

Combine like terms in x^{2}-3y^{2}-2x^{2}+4.

$$\frac{-x^{2}-3y^{2}+4}{xy}$$