Solve (5/4x-5/6x+1/2x)(10/11xy-xy)(frac{1}{3}y+y)

$$( \frac { 5 } { 4 } x - \frac { 5 } { 6 } x + \frac { 1 } { 2 } x ) ( \frac { 10 } { 11 } x y - x y ) ( \frac { 1 } { 3 } y + y )$$

Evaluate

$$-\frac{\left(xy\right)^{2}}{9}$$

Solution Steps

Combine \frac{5}{4}x and -\frac{5}{6}x to get \frac{5}{12}x.

$$\left(\frac{5}{12}x+\frac{1}{2}x\right)\left(\frac{10}{11}xy-xy\right)\left(\frac{1}{3}y+y\right)$$

Combine \frac{5}{12}x and \frac{1}{2}x to get \frac{11}{12}x.

$$\frac{11}{12}x\left(\frac{10}{11}xy-xy\right)\left(\frac{1}{3}y+y\right)$$

Combine \frac{10}{11}xy and -xy to get -\frac{1}{11}xy.

$$\frac{11}{12}x\left(-\frac{1}{11}\right)xy\left(\frac{1}{3}y+y\right)$$

Multiply \frac{11}{12} times -\frac{1}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\left(-1\right)}{12\times 11}xxy\left(\frac{1}{3}y+y\right)$$

Cancel out 11 in both numerator and denominator.

$$\frac{-1}{12}xxy\left(\frac{1}{3}y+y\right)$$

Fraction \frac{-1}{12} can be rewritten as -\frac{1}{12} by extracting the negative sign.

$$-\frac{1}{12}xxy\left(\frac{1}{3}y+y\right)$$

Multiply x and x to get x^{2}.

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

Combine \frac{1}{3}y and y to get \frac{4}{3}y.

$$-\frac{1}{12}x^{2}y\times \frac{4}{3}y$$

Multiply -\frac{1}{12} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-4}{12\times 3}x^{2}yy$$

Do the multiplications in the fraction \frac{-4}{12\times 3}.

$$\frac{-4}{36}x^{2}yy$$

Reduce the fraction \frac{-4}{36} to lowest terms by extracting and canceling out 4.

$$-\frac{1}{9}x^{2}yy$$

Multiply y and y to get y^{2}.

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

Expand

$$-\frac{\left(xy\right)^{2}}{9}$$

Solution Steps

Combine \frac{5}{4}x and -\frac{5}{6}x to get \frac{5}{12}x.

$$\left(\frac{5}{12}x+\frac{1}{2}x\right)\left(\frac{10}{11}xy-xy\right)\left(\frac{1}{3}y+y\right)$$

Combine \frac{5}{12}x and \frac{1}{2}x to get \frac{11}{12}x.

$$\frac{11}{12}x\left(\frac{10}{11}xy-xy\right)\left(\frac{1}{3}y+y\right)$$

Combine \frac{10}{11}xy and -xy to get -\frac{1}{11}xy.

$$\frac{11}{12}x\left(-\frac{1}{11}\right)xy\left(\frac{1}{3}y+y\right)$$

Multiply \frac{11}{12} times -\frac{1}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{11\left(-1\right)}{12\times 11}xxy\left(\frac{1}{3}y+y\right)$$

Cancel out 11 in both numerator and denominator.

$$\frac{-1}{12}xxy\left(\frac{1}{3}y+y\right)$$

Fraction \frac{-1}{12} can be rewritten as -\frac{1}{12} by extracting the negative sign.

$$-\frac{1}{12}xxy\left(\frac{1}{3}y+y\right)$$

Multiply x and x to get x^{2}.

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

Combine \frac{1}{3}y and y to get \frac{4}{3}y.

$$-\frac{1}{12}x^{2}y\times \frac{4}{3}y$$

Multiply -\frac{1}{12} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-4}{12\times 3}x^{2}yy$$

Do the multiplications in the fraction \frac{-4}{12\times 3}.

$$\frac{-4}{36}x^{2}yy$$

Reduce the fraction \frac{-4}{36} to lowest terms by extracting and canceling out 4.

$$-\frac{1}{9}x^{2}yy$$

Multiply y and y to get y^{2}.

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