Solve x+3/x^2+2x-3(x^3-2x+1/x^2+2x-3)

$$\frac { x + 3 } { x ^ { 2 } + 2 x - 3 } ( \frac { x ^ { 3 } - 2 x + 1 } { x ^ { 2 } + 2 x - 3 } )$$

Evaluate

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

Short Solution Steps

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

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

Cancel out x+3 in both numerator and denominator.

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

Factor the expressions that are not already factored in \frac{x^{3}-2x+1}{x^{2}+2x-3}.

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

Cancel out x-1 in both numerator and denominator.

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

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

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

Use the distributive property to multiply x-1 by x+3 and combine like terms.

$$\frac{x^{2}+x-1}{x^{2}+2x-3}$$

Expand

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

Short Solution Steps

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

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

Cancel out x+3 in both numerator and denominator.

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

Factor the expressions that are not already factored in \frac{x^{3}-2x+1}{x^{2}+2x-3}.

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

Cancel out x-1 in both numerator and denominator.

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

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

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

Use the distributive property to multiply x-1 by x+3 and combine like terms.

$$\frac{x^{2}+x-1}{x^{2}+2x-3}$$