Solve =(x+2)(x-7)-(x^3-7)(-1)/(x^3-1)(x-1)

$$= \frac { ( x + 2 ) ( x - 7 ) - ( x ^ { 3 } - 7 ) ( - 1 ) } { ( x ^ { 3 } - 1 ) ( x - 1 ) }$$

Evaluate

$$\frac{\left(x-3\right)\left(x^{2}+4x+7\right)}{\left(x-1\right)^{2}\left(x^{2}+x+1\right)}$$

Short Solution Steps

Use the distributive property to multiply x+2 by x-7 and combine like terms.

$$\frac{x^{2}-5x-14-\left(x^{3}-7\right)\left(-1\right)}{\left(x^{3}-1\right)\left(x-1\right)}$$

Use the distributive property to multiply x^{3}-7 by -1.

$$\frac{x^{2}-5x-14-\left(-x^{3}+7\right)}{\left(x^{3}-1\right)\left(x-1\right)}$$

To find the opposite of -x^{3}+7, find the opposite of each term.

$$\frac{x^{2}-5x-14+x^{3}-7}{\left(x^{3}-1\right)\left(x-1\right)}$$

Subtract 7 from -14 to get -21.

$$\frac{x^{2}-5x-21+x^{3}}{\left(x^{3}-1\right)\left(x-1\right)}$$

Use the distributive property to multiply x^{3}-1 by x-1.

$$\frac{x^{2}-5x-21+x^{3}}{x^{4}-x^{3}-x+1}$$

Expand

$$\frac{x^{3}+x^{2}-5x-21}{\left(x-1\right)\left(x^{3}-1\right)}$$

Short Solution Steps

Use the distributive property to multiply x+2 by x-7 and combine like terms.

$$\frac{x^{2}-5x-14-\left(x^{3}-7\right)\left(-1\right)}{\left(x^{3}-1\right)\left(x-1\right)}$$

Use the distributive property to multiply x^{3}-7 by -1.

$$\frac{x^{2}-5x-14-\left(-x^{3}+7\right)}{\left(x^{3}-1\right)\left(x-1\right)}$$

To find the opposite of -x^{3}+7, find the opposite of each term.

$$\frac{x^{2}-5x-14+x^{3}-7}{\left(x^{3}-1\right)\left(x-1\right)}$$

Subtract 7 from -14 to get -21.

$$\frac{x^{2}-5x-21+x^{3}}{\left(x^{3}-1\right)\left(x-1\right)}$$

Use the distributive property to multiply x^{3}-1 by x-1.

$$\frac{x^{2}-5x-21+x^{3}}{x^{4}-x^{3}-x+1}$$