Solve (9/4x^{2}-y^{2})+(-2/3x^2+7/2y^2)-(3/4x^2+frac{1}{6}y^2)

$$( \frac { 9 } { 4 } x ^ { 2 } - y ^ { 2 } ) + ( - \frac { 2 } { 3 } x ^ { 2 } + \frac { 7 } { 2 } y ^ { 2 } ) - ( \frac { 3 } { 4 } x ^ { 2 } + \frac { 1 } { 6 } y ^ { 2 } )$$

Evaluate

$$\frac{5x^{2}}{6}+\frac{7y^{2}}{3}$$

Solution Steps

Combine \frac{9}{4}x^{2} and -\frac{2}{3}x^{2} to get \frac{19}{12}x^{2}.

$$\frac{19}{12}x^{2}-y^{2}+\frac{7}{2}y^{2}-\left(\frac{3}{4}x^{2}+\frac{1}{6}y^{2}\right)$$

Combine -y^{2} and \frac{7}{2}y^{2} to get \frac{5}{2}y^{2}.

$$\frac{19}{12}x^{2}+\frac{5}{2}y^{2}-\left(\frac{3}{4}x^{2}+\frac{1}{6}y^{2}\right)$$

To find the opposite of \frac{3}{4}x^{2}+\frac{1}{6}y^{2}, find the opposite of each term.

$$\frac{19}{12}x^{2}+\frac{5}{2}y^{2}-\frac{3}{4}x^{2}-\frac{1}{6}y^{2}$$

Combine \frac{19}{12}x^{2} and -\frac{3}{4}x^{2} to get \frac{5}{6}x^{2}.

$$\frac{5}{6}x^{2}+\frac{5}{2}y^{2}-\frac{1}{6}y^{2}$$

Combine \frac{5}{2}y^{2} and -\frac{1}{6}y^{2} to get \frac{7}{3}y^{2}.

$$\frac{5}{6}x^{2}+\frac{7}{3}y^{2}$$

Expand

$$\frac{5x^{2}}{6}+\frac{7y^{2}}{3}$$

Solution Steps

Combine \frac{9}{4}x^{2} and -\frac{2}{3}x^{2} to get \frac{19}{12}x^{2}.

$$\frac{19}{12}x^{2}-y^{2}+\frac{7}{2}y^{2}-\left(\frac{3}{4}x^{2}+\frac{1}{6}y^{2}\right)$$

Combine -y^{2} and \frac{7}{2}y^{2} to get \frac{5}{2}y^{2}.

$$\frac{19}{12}x^{2}+\frac{5}{2}y^{2}-\left(\frac{3}{4}x^{2}+\frac{1}{6}y^{2}\right)$$

To find the opposite of \frac{3}{4}x^{2}+\frac{1}{6}y^{2}, find the opposite of each term.

$$\frac{19}{12}x^{2}+\frac{5}{2}y^{2}-\frac{3}{4}x^{2}-\frac{1}{6}y^{2}$$

Combine \frac{19}{12}x^{2} and -\frac{3}{4}x^{2} to get \frac{5}{6}x^{2}.

$$\frac{5}{6}x^{2}+\frac{5}{2}y^{2}-\frac{1}{6}y^{2}$$

Combine \frac{5}{2}y^{2} and -\frac{1}{6}y^{2} to get \frac{7}{3}y^{2}.

$$\frac{5}{6}x^{2}+\frac{7}{3}y^{2}$$