Solve frac{x^{2}+3x+2}{x^{4}y}*frac{x^{5}y^2+3x^4y^2}{x^2+4x+3}

$$\frac { x ^ { 2 } + 3 x + 2 } { x ^ { 4 } y } \cdot \frac { x ^ { 5 } y ^ { 2 } + 3 x ^ { 4 } y ^ { 2 } } { x ^ { 2 } + 4 x + 3 }$$

Evaluate

$$y\left(x+2\right)$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{5}y^{2}+3x^{4}y^{2}}{x^{2}+4x+3}.

$$\frac{x^{2}+3x+2}{x^{4}y}\times \frac{\left(x+3\right)y^{2}x^{4}}{\left(x+1\right)\left(x+3\right)}$$

Cancel out x+3 in both numerator and denominator.

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

Multiply \frac{x^{2}+3x+2}{x^{4}y} times \frac{y^{2}x^{4}}{x+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}+3x+2\right)y^{2}x^{4}}{x^{4}y\left(x+1\right)}$$

Cancel out yx^{4} in both numerator and denominator.

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

Factor the expressions that are not already factored.

$$\frac{y\left(x+1\right)\left(x+2\right)}{x+1}$$

Cancel out x+1 in both numerator and denominator.

$$y\left(x+2\right)$$

Expand the expression.

$$xy+2y$$

Expand

$$xy+2y$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{5}y^{2}+3x^{4}y^{2}}{x^{2}+4x+3}.

$$\frac{x^{2}+3x+2}{x^{4}y}\times \frac{\left(x+3\right)y^{2}x^{4}}{\left(x+1\right)\left(x+3\right)}$$

Cancel out x+3 in both numerator and denominator.

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

Multiply \frac{x^{2}+3x+2}{x^{4}y} times \frac{y^{2}x^{4}}{x+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}+3x+2\right)y^{2}x^{4}}{x^{4}y\left(x+1\right)}$$

Cancel out yx^{4} in both numerator and denominator.

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

Factor the expressions that are not already factored.

$$\frac{y\left(x+1\right)\left(x+2\right)}{x+1}$$

Cancel out x+1 in both numerator and denominator.

$$y\left(x+2\right)$$

Expand the expression.

$$xy+2y$$