Solve (5/4x^{4}y^{2}-2x^{4}y^{2}+1/2x^{4}y^{2}):(-5/8x^{2}y^{2}+1/4x^{2}y^{2}-frac{2}{5}x^2y^2-frac{9}{40}x^2y^2)

$$( \frac { 5 } { 4 } x ^ { 4 } y ^ { 2 } - 2 x ^ { 4 } y ^ { 2 } + \frac { 1 } { 2 } x ^ { 4 } y ^ { 2 } ) : ( - \frac { 5 } { 8 } x ^ { 2 } y ^ { 2 } + \frac { 1 } { 4 } x ^ { 2 } y ^ { 2 } - \frac { 2 } { 5 } x ^ { 2 } y ^ { 2 } - \frac { 9 } { 40 } x ^ { 2 } y ^ { 2 } )$$

Evaluate

$$\frac{x^{2}}{4}$$

Solution Steps

Combine \frac{5}{4}x^{4}y^{2} and -2x^{4}y^{2} to get -\frac{3}{4}x^{4}y^{2}.

$$\frac{-\frac{3}{4}x^{4}y^{2}+\frac{1}{2}x^{4}y^{2}}{-\frac{5}{8}x^{2}y^{2}+\frac{1}{4}x^{2}y^{2}-\frac{2}{5}x^{2}y^{2}-\frac{9}{40}x^{2}y^{2}}$$

Combine -\frac{3}{4}x^{4}y^{2} and \frac{1}{2}x^{4}y^{2} to get -\frac{1}{4}x^{4}y^{2}.

$$\frac{-\frac{1}{4}x^{4}y^{2}}{-\frac{5}{8}x^{2}y^{2}+\frac{1}{4}x^{2}y^{2}-\frac{2}{5}x^{2}y^{2}-\frac{9}{40}x^{2}y^{2}}$$

Combine -\frac{5}{8}x^{2}y^{2} and \frac{1}{4}x^{2}y^{2} to get -\frac{3}{8}x^{2}y^{2}.

$$\frac{-\frac{1}{4}x^{4}y^{2}}{-\frac{3}{8}x^{2}y^{2}-\frac{2}{5}x^{2}y^{2}-\frac{9}{40}x^{2}y^{2}}$$

Combine -\frac{3}{8}x^{2}y^{2} and -\frac{2}{5}x^{2}y^{2} to get -\frac{31}{40}x^{2}y^{2}.

$$\frac{-\frac{1}{4}x^{4}y^{2}}{-\frac{31}{40}x^{2}y^{2}-\frac{9}{40}x^{2}y^{2}}$$

Combine -\frac{31}{40}x^{2}y^{2} and -\frac{9}{40}x^{2}y^{2} to get -x^{2}y^{2}.

$$\frac{-\frac{1}{4}x^{4}y^{2}}{-x^{2}y^{2}}$$

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

$$\frac{-\frac{1}{4}x^{2}}{-1}$$

Anything divided by -1 gives its opposite.

$$\frac{1}{4}x^{2}$$

Expand

$$\frac{x^{2}}{4}$$

Solution Steps

Combine \frac{5}{4}x^{4}y^{2} and -2x^{4}y^{2} to get -\frac{3}{4}x^{4}y^{2}.

$$\frac{-\frac{3}{4}x^{4}y^{2}+\frac{1}{2}x^{4}y^{2}}{-\frac{5}{8}x^{2}y^{2}+\frac{1}{4}x^{2}y^{2}-\frac{2}{5}x^{2}y^{2}-\frac{9}{40}x^{2}y^{2}}$$

Combine -\frac{3}{4}x^{4}y^{2} and \frac{1}{2}x^{4}y^{2} to get -\frac{1}{4}x^{4}y^{2}.

$$\frac{-\frac{1}{4}x^{4}y^{2}}{-\frac{5}{8}x^{2}y^{2}+\frac{1}{4}x^{2}y^{2}-\frac{2}{5}x^{2}y^{2}-\frac{9}{40}x^{2}y^{2}}$$

Combine -\frac{5}{8}x^{2}y^{2} and \frac{1}{4}x^{2}y^{2} to get -\frac{3}{8}x^{2}y^{2}.

$$\frac{-\frac{1}{4}x^{4}y^{2}}{-\frac{3}{8}x^{2}y^{2}-\frac{2}{5}x^{2}y^{2}-\frac{9}{40}x^{2}y^{2}}$$

Combine -\frac{3}{8}x^{2}y^{2} and -\frac{2}{5}x^{2}y^{2} to get -\frac{31}{40}x^{2}y^{2}.

$$\frac{-\frac{1}{4}x^{4}y^{2}}{-\frac{31}{40}x^{2}y^{2}-\frac{9}{40}x^{2}y^{2}}$$

Combine -\frac{31}{40}x^{2}y^{2} and -\frac{9}{40}x^{2}y^{2} to get -x^{2}y^{2}.

$$\frac{-\frac{1}{4}x^{4}y^{2}}{-x^{2}y^{2}}$$

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

$$\frac{-\frac{1}{4}x^{2}}{-1}$$

Anything divided by -1 gives its opposite.

$$\frac{1}{4}x^{2}$$