Solve 3x-xy/4xy*4y+12/9-y^2

$$\frac { 3 x - x y } { 4 x y } \times \frac { 4 y + 12 } { 9 - y ^ { 2 } }$$

Evaluate

$$\frac{1}{y}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3x-xy}{4xy}.

$$\frac{x\left(-y+3\right)}{4xy}\times \frac{4y+12}{9-y^{2}}$$

Cancel out x in both numerator and denominator.

$$\frac{-y+3}{4y}\times \frac{4y+12}{9-y^{2}}$$

Factor the expressions that are not already factored in \frac{4y+12}{9-y^{2}}.

$$\frac{-y+3}{4y}\times \frac{4\left(y+3\right)}{\left(y-3\right)\left(-y-3\right)}$$

Extract the negative sign in 3+y.

$$\frac{-y+3}{4y}\times \frac{-4\left(-y-3\right)}{\left(y-3\right)\left(-y-3\right)}$$

Cancel out -y-3 in both numerator and denominator.

$$\frac{-y+3}{4y}\times \frac{-4}{y-3}$$

Multiply \frac{-y+3}{4y} times \frac{-4}{y-3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(-y+3\right)\left(-4\right)}{4y\left(y-3\right)}$$

Extract the negative sign in -y+3.

$$\frac{-4\left(-1\right)\left(y-3\right)}{4y\left(y-3\right)}$$

Cancel out 4\left(y-3\right) in both numerator and denominator.

$$\frac{-\left(-1\right)}{y}$$

Multiply -1 and -1 to get 1.

$$\frac{1}{y}$$

Expand

$$\frac{1}{y}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3x-xy}{4xy}.

$$\frac{x\left(-y+3\right)}{4xy}\times \frac{4y+12}{9-y^{2}}$$

Cancel out x in both numerator and denominator.

$$\frac{-y+3}{4y}\times \frac{4y+12}{9-y^{2}}$$

Factor the expressions that are not already factored in \frac{4y+12}{9-y^{2}}.

$$\frac{-y+3}{4y}\times \frac{4\left(y+3\right)}{\left(y-3\right)\left(-y-3\right)}$$

Extract the negative sign in 3+y.

$$\frac{-y+3}{4y}\times \frac{-4\left(-y-3\right)}{\left(y-3\right)\left(-y-3\right)}$$

Cancel out -y-3 in both numerator and denominator.

$$\frac{-y+3}{4y}\times \frac{-4}{y-3}$$

Multiply \frac{-y+3}{4y} times \frac{-4}{y-3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(-y+3\right)\left(-4\right)}{4y\left(y-3\right)}$$

Extract the negative sign in -y+3.

$$\frac{-4\left(-1\right)\left(y-3\right)}{4y\left(y-3\right)}$$

Cancel out 4\left(y-3\right) in both numerator and denominator.

$$\frac{-\left(-1\right)}{y}$$

Multiply -1 and -1 to get 1.

$$\frac{1}{y}$$