Solve x-6/x^2+11x+24{frac{x+1/x+3}}

$$\frac{ x-6 }{ \frac{ { x }^{ 2 } +11x+24 }{ \frac{ x+1 }{ x+3 } } }$$

Evaluate

$$\frac{\left(x-6\right)\left(x+1\right)}{\left(x+8\right)\left(x+3\right)^{2}}$$

Short Solution Steps

Divide x-6 by \frac{x^{2}+11x+24}{\frac{x+1}{x+3}} by multiplying x-6 by the reciprocal of \frac{x^{2}+11x+24}{\frac{x+1}{x+3}}.

$$\frac{\left(x-6\right)\times \frac{x+1}{x+3}}{x^{2}+11x+24}$$

Express \left(x-6\right)\times \frac{x+1}{x+3} as a single fraction.

$$\frac{\frac{\left(x-6\right)\left(x+1\right)}{x+3}}{x^{2}+11x+24}$$

Express \frac{\frac{\left(x-6\right)\left(x+1\right)}{x+3}}{x^{2}+11x+24} as a single fraction.

$$\frac{\left(x-6\right)\left(x+1\right)}{\left(x+3\right)\left(x^{2}+11x+24\right)}$$

Use the distributive property to multiply x-6 by x+1 and combine like terms.

$$\frac{x^{2}-5x-6}{\left(x+3\right)\left(x^{2}+11x+24\right)}$$

Use the distributive property to multiply x+3 by x^{2}+11x+24 and combine like terms.

$$\frac{x^{2}-5x-6}{x^{3}+14x^{2}+57x+72}$$

Expand

$$\frac{x^{2}-5x-6}{\left(x+3\right)\left(x^{2}+11x+24\right)}$$

Short Solution Steps

Divide x-6 by \frac{x^{2}+11x+24}{\frac{x+1}{x+3}} by multiplying x-6 by the reciprocal of \frac{x^{2}+11x+24}{\frac{x+1}{x+3}}.

$$\frac{\left(x-6\right)\times \frac{x+1}{x+3}}{x^{2}+11x+24}$$

Express \left(x-6\right)\times \frac{x+1}{x+3} as a single fraction.

$$\frac{\frac{\left(x-6\right)\left(x+1\right)}{x+3}}{x^{2}+11x+24}$$

Express \frac{\frac{\left(x-6\right)\left(x+1\right)}{x+3}}{x^{2}+11x+24} as a single fraction.

$$\frac{\left(x-6\right)\left(x+1\right)}{\left(x+3\right)\left(x^{2}+11x+24\right)}$$

Use the distributive property to multiply x-6 by x+1 and combine like terms.

$$\frac{x^{2}-5x-6}{\left(x+3\right)\left(x^{2}+11x+24\right)}$$

Use the distributive property to multiply x+3 by x^{2}+11x+24 and combine like terms.

$$\frac{x^{2}-5x-6}{x^{3}+14x^{2}+57x+72}$$