Solve x^2+3x-10/x^2+8x+15*x^2+5x+6/x^2+4x+4

$$\frac { x ^ { 2 } + 3 x - 10 } { x ^ { 2 } + 8 x + 15 } \cdot \frac { x ^ { 2 } + 5 x + 6 } { x ^ { 2 } + 4 x + 4 }$$

Evaluate

$$\frac{x-2}{x+2}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}+3x-10}{x^{2}+8x+15}.

$$\frac{\left(x-2\right)\left(x+5\right)}{\left(x+3\right)\left(x+5\right)}\times \frac{x^{2}+5x+6}{x^{2}+4x+4}$$

Cancel out x+5 in both numerator and denominator.

$$\frac{x-2}{x+3}\times \frac{x^{2}+5x+6}{x^{2}+4x+4}$$

Factor the expressions that are not already factored in \frac{x^{2}+5x+6}{x^{2}+4x+4}.

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

Cancel out x+2 in both numerator and denominator.

$$\frac{x-2}{x+3}\times \frac{x+3}{x+2}$$

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

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

Cancel out x+3 in both numerator and denominator.

$$\frac{x-2}{x+2}$$

Expand

$$\frac{x-2}{x+2}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}+3x-10}{x^{2}+8x+15}.

$$\frac{\left(x-2\right)\left(x+5\right)}{\left(x+3\right)\left(x+5\right)}\times \frac{x^{2}+5x+6}{x^{2}+4x+4}$$

Cancel out x+5 in both numerator and denominator.

$$\frac{x-2}{x+3}\times \frac{x^{2}+5x+6}{x^{2}+4x+4}$$

Factor the expressions that are not already factored in \frac{x^{2}+5x+6}{x^{2}+4x+4}.

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

Cancel out x+2 in both numerator and denominator.

$$\frac{x-2}{x+3}\times \frac{x+3}{x+2}$$

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

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

Cancel out x+3 in both numerator and denominator.

$$\frac{x-2}{x+2}$$