Solve (x-3)(x^2-7x-30)/(x+2)(x^2+4x+3)/(x+3)(x-10)/x^2+x-2

$$\frac{ \frac{ \frac{ (x-3)( { x }^{ 2 } -7x-30) }{ (x+2)( { x }^{ 2 } +4x+3) } }{ (x+3)(x-10) } }{ { x }^{ 2 } +x-2 }$$

Evaluate

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

Short Solution Steps

Express \frac{\frac{\frac{\left(x-3\right)\left(x^{2}-7x-30\right)}{\left(x+2\right)\left(x^{2}+4x+3\right)}}{\left(x+3\right)\left(x-10\right)}}{x^{2}+x-2} as a single fraction.

$$\frac{\frac{\left(x-3\right)\left(x^{2}-7x-30\right)}{\left(x+2\right)\left(x^{2}+4x+3\right)}}{\left(x+3\right)\left(x-10\right)\left(x^{2}+x-2\right)}$$

Factor the expressions that are not already factored in \frac{\left(x-3\right)\left(x^{2}-7x-30\right)}{\left(x+2\right)\left(x^{2}+4x+3\right)}.

$$\frac{\frac{\left(x-10\right)\left(x-3\right)\left(x+3\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}}{\left(x+3\right)\left(x-10\right)\left(x^{2}+x-2\right)}$$

Cancel out x+3 in both numerator and denominator.

$$\frac{\frac{\left(x-10\right)\left(x-3\right)}{\left(x+1\right)\left(x+2\right)}}{\left(x+3\right)\left(x-10\right)\left(x^{2}+x-2\right)}$$

Express \frac{\frac{\left(x-10\right)\left(x-3\right)}{\left(x+1\right)\left(x+2\right)}}{\left(x+3\right)\left(x-10\right)\left(x^{2}+x-2\right)} as a single fraction.

$$\frac{\left(x-10\right)\left(x-3\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x-10\right)\left(x^{2}+x-2\right)}$$

Cancel out x-10 in both numerator and denominator.

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

Use the distributive property to multiply x+1 by x+2 and combine like terms.

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

Use the distributive property to multiply x^{2}+3x+2 by x+3 and combine like terms.

$$\frac{x-3}{\left(x^{3}+6x^{2}+11x+6\right)\left(x^{2}+x-2\right)}$$

Use the distributive property to multiply x^{3}+6x^{2}+11x+6 by x^{2}+x-2 and combine like terms.

$$\frac{x-3}{x^{5}+7x^{4}+15x^{3}+5x^{2}-16x-12}$$

Expand

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

Short Solution Steps

Express \frac{\frac{\frac{\left(x-3\right)\left(x^{2}-7x-30\right)}{\left(x+2\right)\left(x^{2}+4x+3\right)}}{\left(x+3\right)\left(x-10\right)}}{x^{2}+x-2} as a single fraction.

$$\frac{\frac{\left(x-3\right)\left(x^{2}-7x-30\right)}{\left(x+2\right)\left(x^{2}+4x+3\right)}}{\left(x+3\right)\left(x-10\right)\left(x^{2}+x-2\right)}$$

Factor the expressions that are not already factored in \frac{\left(x-3\right)\left(x^{2}-7x-30\right)}{\left(x+2\right)\left(x^{2}+4x+3\right)}.

$$\frac{\frac{\left(x-10\right)\left(x-3\right)\left(x+3\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)}}{\left(x+3\right)\left(x-10\right)\left(x^{2}+x-2\right)}$$

Cancel out x+3 in both numerator and denominator.

$$\frac{\frac{\left(x-10\right)\left(x-3\right)}{\left(x+1\right)\left(x+2\right)}}{\left(x+3\right)\left(x-10\right)\left(x^{2}+x-2\right)}$$

Express \frac{\frac{\left(x-10\right)\left(x-3\right)}{\left(x+1\right)\left(x+2\right)}}{\left(x+3\right)\left(x-10\right)\left(x^{2}+x-2\right)} as a single fraction.

$$\frac{\left(x-10\right)\left(x-3\right)}{\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x-10\right)\left(x^{2}+x-2\right)}$$

Cancel out x-10 in both numerator and denominator.

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

Use the distributive property to multiply x+1 by x+2 and combine like terms.

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

Use the distributive property to multiply x^{2}+3x+2 by x+3 and combine like terms.

$$\frac{x-3}{\left(x^{3}+6x^{2}+11x+6\right)\left(x^{2}+x-2\right)}$$

Use the distributive property to multiply x^{3}+6x^{2}+11x+6 by x^{2}+x-2 and combine like terms.

$$\frac{x-3}{x^{5}+7x^{4}+15x^{3}+5x^{2}-16x-12}$$