Solve 2xy+2y^2/21y^2z-42xyzdiv5x^2+5xy/28x-14y

$$\frac { 2 x y + 2 y ^ { 2 } } { 21 y ^ { 2 } z - 42 x y z } \div \frac { 5 x ^ { 2 } + 5 x y } { 28 x - 14 y }$$

Evaluate

$$-\frac{4}{15xz}$$

Short Solution Steps

Divide \frac{2xy+2y^{2}}{21y^{2}z-42xyz} by \frac{5x^{2}+5xy}{28x-14y} by multiplying \frac{2xy+2y^{2}}{21y^{2}z-42xyz} by the reciprocal of \frac{5x^{2}+5xy}{28x-14y}.

$$\frac{\left(2xy+2y^{2}\right)\left(28x-14y\right)}{\left(21y^{2}z-42xyz\right)\left(5x^{2}+5xy\right)}$$

Factor the expressions that are not already factored.

$$\frac{2\times 14y\left(x+y\right)\left(2x-y\right)}{5\times 21xyz\left(x+y\right)\left(-2x+y\right)}$$

Extract the negative sign in 2x-y.

$$\frac{-2\times 14y\left(x+y\right)\left(-2x+y\right)}{5\times 21xyz\left(x+y\right)\left(-2x+y\right)}$$

Cancel out 7y\left(x+y\right)\left(-2x+y\right) in both numerator and denominator.

$$\frac{-2\times 2}{3\times 5xz}$$

Expand the expression.

$$\frac{-4}{15xz}$$

Expand

$$-\frac{4}{15xz}$$

Short Solution Steps

Divide \frac{2xy+2y^{2}}{21y^{2}z-42xyz} by \frac{5x^{2}+5xy}{28x-14y} by multiplying \frac{2xy+2y^{2}}{21y^{2}z-42xyz} by the reciprocal of \frac{5x^{2}+5xy}{28x-14y}.

$$\frac{\left(2xy+2y^{2}\right)\left(28x-14y\right)}{\left(21y^{2}z-42xyz\right)\left(5x^{2}+5xy\right)}$$

Factor the expressions that are not already factored.

$$\frac{2\times 14y\left(x+y\right)\left(2x-y\right)}{5\times 21xyz\left(x+y\right)\left(-2x+y\right)}$$

Extract the negative sign in 2x-y.

$$\frac{-2\times 14y\left(x+y\right)\left(-2x+y\right)}{5\times 21xyz\left(x+y\right)\left(-2x+y\right)}$$

Cancel out 7y\left(x+y\right)\left(-2x+y\right) in both numerator and denominator.

$$\frac{-2\times 2}{3\times 5xz}$$

Expand the expression.

$$\frac{-4}{15xz}$$