Solve x^2+x/2x+3*3x^2+19x+28/x^2+5x+4

$$\frac { x ^ { 2 } + x } { 2 x + 3 } \times \frac { 3 x ^ { 2 } + 19 x + 28 } { x ^ { 2 } + 5 x + 4 }$$

Evaluate

$$\frac{x\left(3x+7\right)}{2x+3}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3x^{2}+19x+28}{x^{2}+5x+4}.

$$\frac{x^{2}+x}{2x+3}\times \frac{\left(x+4\right)\left(3x+7\right)}{\left(x+1\right)\left(x+4\right)}$$

Cancel out x+4 in both numerator and denominator.

$$\frac{x^{2}+x}{2x+3}\times \frac{3x+7}{x+1}$$

Multiply \frac{x^{2}+x}{2x+3} times \frac{3x+7}{x+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}+x\right)\left(3x+7\right)}{\left(2x+3\right)\left(x+1\right)}$$

Factor the expressions that are not already factored.

$$\frac{x\left(x+1\right)\left(3x+7\right)}{\left(x+1\right)\left(2x+3\right)}$$

Cancel out x+1 in both numerator and denominator.

$$\frac{x\left(3x+7\right)}{2x+3}$$

Expand the expression.

$$\frac{3x^{2}+7x}{2x+3}$$

Expand

$$\frac{3x^{2}+7x}{2x+3}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3x^{2}+19x+28}{x^{2}+5x+4}.

$$\frac{x^{2}+x}{2x+3}\times \frac{\left(x+4\right)\left(3x+7\right)}{\left(x+1\right)\left(x+4\right)}$$

Cancel out x+4 in both numerator and denominator.

$$\frac{x^{2}+x}{2x+3}\times \frac{3x+7}{x+1}$$

Multiply \frac{x^{2}+x}{2x+3} times \frac{3x+7}{x+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}+x\right)\left(3x+7\right)}{\left(2x+3\right)\left(x+1\right)}$$

Factor the expressions that are not already factored.

$$\frac{x\left(x+1\right)\left(3x+7\right)}{\left(x+1\right)\left(2x+3\right)}$$

Cancel out x+1 in both numerator and denominator.

$$\frac{x\left(3x+7\right)}{2x+3}$$

Expand the expression.

$$\frac{3x^{2}+7x}{2x+3}$$