Solve (-2/3x)*(-6/5y)-4/5xy+(-2/5)*(frac{5}{4}xy)+xy-2xy

$$( - \frac { 2 } { 3 } x ) \cdot ( - \frac { 6 } { 5 } y ) - \frac { 4 } { 5 } x y + ( - \frac { 2 } { 5 } ) \cdot ( \frac { 5 } { 4 } x y ) + x y - 2 x y$$

Evaluate

$$-\frac{3xy}{2}$$

Solution Steps

Multiply -\frac{2}{3} times -\frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2\left(-6\right)}{3\times 5}xy-\frac{4}{5}xy-\frac{2}{5}\times \frac{5}{4}xy+xy-2xy$$

Do the multiplications in the fraction \frac{-2\left(-6\right)}{3\times 5}.

$$\frac{12}{15}xy-\frac{4}{5}xy-\frac{2}{5}\times \frac{5}{4}xy+xy-2xy$$

Reduce the fraction \frac{12}{15} to lowest terms by extracting and canceling out 3.

$$\frac{4}{5}xy-\frac{4}{5}xy-\frac{2}{5}\times \frac{5}{4}xy+xy-2xy$$

Combine \frac{4}{5}xy and -\frac{4}{5}xy to get 0.

$$-\frac{2}{5}\times \frac{5}{4}xy+xy-2xy$$

Multiply -\frac{2}{5} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2\times 5}{5\times 4}xy+xy-2xy$$

Cancel out 5 in both numerator and denominator.

$$\frac{-2}{4}xy+xy-2xy$$

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

$$-\frac{1}{2}xy+xy-2xy$$

Combine -\frac{1}{2}xy and xy to get \frac{1}{2}xy.

$$\frac{1}{2}xy-2xy$$

Combine \frac{1}{2}xy and -2xy to get -\frac{3}{2}xy.

$$-\frac{3}{2}xy$$

Differentiate w.r.t. x

$$-\frac{3y}{2}$$