Solve x^2+2x-3/x^2-3x+2*x^2+2x-8/x^2+4x+3

$$\frac { x ^ { 2 } + 2 x - 3 } { x ^ { 2 } - 3 x + 2 } \cdot \frac { x ^ { 2 } + 2 x - 8 } { x ^ { 2 } + 4 x + 3 }$$

Evaluate

$$\frac{x+4}{x+1}$$

Short Solution Steps

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

$$\frac{\left(x-1\right)\left(x+3\right)}{\left(x-2\right)\left(x-1\right)}\times \frac{x^{2}+2x-8}{x^{2}+4x+3}$$

Cancel out x-1 in both numerator and denominator.

$$\frac{x+3}{x-2}\times \frac{x^{2}+2x-8}{x^{2}+4x+3}$$

Multiply \frac{x+3}{x-2} times \frac{x^{2}+2x-8}{x^{2}+4x+3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+3\right)\left(x^{2}+2x-8\right)}{\left(x-2\right)\left(x^{2}+4x+3\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(x-2\right)\left(x+3\right) in both numerator and denominator.

$$\frac{x+4}{x+1}$$

Expand

$$\frac{x+4}{x+1}$$

Short Solution Steps

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

$$\frac{\left(x-1\right)\left(x+3\right)}{\left(x-2\right)\left(x-1\right)}\times \frac{x^{2}+2x-8}{x^{2}+4x+3}$$

Cancel out x-1 in both numerator and denominator.

$$\frac{x+3}{x-2}\times \frac{x^{2}+2x-8}{x^{2}+4x+3}$$

Multiply \frac{x+3}{x-2} times \frac{x^{2}+2x-8}{x^{2}+4x+3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+3\right)\left(x^{2}+2x-8\right)}{\left(x-2\right)\left(x^{2}+4x+3\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(x-2\right)\left(x+3\right) in both numerator and denominator.

$$\frac{x+4}{x+1}$$