Evaluate
\frac{x^{2}-6xy-6y}{8}
Expand
-\frac{3xy}{4}+\frac{x^{2}}{8}-\frac{3y}{4}
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-\frac{2}{3}xy+\frac{3}{4}x^{2}-\frac{3}{5}y-\left(\frac{73}{60}y+\frac{5}{8}x^{2}\right)-\frac{1}{12}xy+\frac{16}{15}y
Combine \frac{3}{4}y and \frac{7}{15}y to get \frac{73}{60}y.
-\frac{2}{3}xy+\frac{3}{4}x^{2}-\frac{3}{5}y-\frac{73}{60}y-\frac{5}{8}x^{2}-\frac{1}{12}xy+\frac{16}{15}y
To find the opposite of \frac{73}{60}y+\frac{5}{8}x^{2}, find the opposite of each term.
-\frac{2}{3}xy+\frac{3}{4}x^{2}-\frac{109}{60}y-\frac{5}{8}x^{2}-\frac{1}{12}xy+\frac{16}{15}y
Combine -\frac{3}{5}y and -\frac{73}{60}y to get -\frac{109}{60}y.
-\frac{2}{3}xy+\frac{1}{8}x^{2}-\frac{109}{60}y-\frac{1}{12}xy+\frac{16}{15}y
Combine \frac{3}{4}x^{2} and -\frac{5}{8}x^{2} to get \frac{1}{8}x^{2}.
-\frac{3}{4}xy+\frac{1}{8}x^{2}-\frac{109}{60}y+\frac{16}{15}y
Combine -\frac{2}{3}xy and -\frac{1}{12}xy to get -\frac{3}{4}xy.
-\frac{3}{4}xy+\frac{1}{8}x^{2}-\frac{3}{4}y
Combine -\frac{109}{60}y and \frac{16}{15}y to get -\frac{3}{4}y.
-\frac{2}{3}xy+\frac{3}{4}x^{2}-\frac{3}{5}y-\left(\frac{73}{60}y+\frac{5}{8}x^{2}\right)-\frac{1}{12}xy+\frac{16}{15}y
Combine \frac{3}{4}y and \frac{7}{15}y to get \frac{73}{60}y.
-\frac{2}{3}xy+\frac{3}{4}x^{2}-\frac{3}{5}y-\frac{73}{60}y-\frac{5}{8}x^{2}-\frac{1}{12}xy+\frac{16}{15}y
To find the opposite of \frac{73}{60}y+\frac{5}{8}x^{2}, find the opposite of each term.
-\frac{2}{3}xy+\frac{3}{4}x^{2}-\frac{109}{60}y-\frac{5}{8}x^{2}-\frac{1}{12}xy+\frac{16}{15}y
Combine -\frac{3}{5}y and -\frac{73}{60}y to get -\frac{109}{60}y.
-\frac{2}{3}xy+\frac{1}{8}x^{2}-\frac{109}{60}y-\frac{1}{12}xy+\frac{16}{15}y
Combine \frac{3}{4}x^{2} and -\frac{5}{8}x^{2} to get \frac{1}{8}x^{2}.
-\frac{3}{4}xy+\frac{1}{8}x^{2}-\frac{109}{60}y+\frac{16}{15}y
Combine -\frac{2}{3}xy and -\frac{1}{12}xy to get -\frac{3}{4}xy.
-\frac{3}{4}xy+\frac{1}{8}x^{2}-\frac{3}{4}y
Combine -\frac{109}{60}y and \frac{16}{15}y to get -\frac{3}{4}y.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}