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

$$\frac { x ^ { 2 } + 4 x y + 3 y ^ { 2 } } { x ^ { 2 } - y ^ { 2 } } \cdot \frac { x ^ { 2 } + x y } { x - y } \div \frac { x ^ { 2 } + 3 x } { ( x - y ) }$$

Evaluate

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

Short Solution Steps

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

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

Cancel out x+y in both numerator and denominator.

$$\frac{\frac{x+3y}{x-y}\times \frac{x^{2}+xy}{x-y}}{\frac{x^{2}+3x}{x-y}}$$

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

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

Divide \frac{\left(x+3y\right)\left(x^{2}+xy\right)}{\left(x-y\right)\left(x-y\right)} by \frac{x^{2}+3x}{x-y} by multiplying \frac{\left(x+3y\right)\left(x^{2}+xy\right)}{\left(x-y\right)\left(x-y\right)} by the reciprocal of \frac{x^{2}+3x}{x-y}.

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

Cancel out x-y in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x in both numerator and denominator.

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

Expand the expression.

$$\frac{x^{2}+4xy+3y^{2}}{x^{2}-xy+3x-3y}$$

Expand

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

Short Solution Steps

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

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

Cancel out x+y in both numerator and denominator.

$$\frac{\frac{x+3y}{x-y}\times \frac{x^{2}+xy}{x-y}}{\frac{x^{2}+3x}{x-y}}$$

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

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

Divide \frac{\left(x+3y\right)\left(x^{2}+xy\right)}{\left(x-y\right)\left(x-y\right)} by \frac{x^{2}+3x}{x-y} by multiplying \frac{\left(x+3y\right)\left(x^{2}+xy\right)}{\left(x-y\right)\left(x-y\right)} by the reciprocal of \frac{x^{2}+3x}{x-y}.

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

Cancel out x-y in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x in both numerator and denominator.

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

Expand the expression.

$$\frac{x^{2}+4xy+3y^{2}}{x^{2}-xy+3x-3y}$$