Solve 11/x^2+7x-8-1/x-1/frac{2{x+8}+1}

$$\frac { \frac { 11 } { x ^ { 2 } + 7 x - 8 } - \frac { 1 } { x - 1 } } { \frac { 2 } { x + 8 } + 1 }$$

Evaluate

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

Short Solution Steps

Factor x^{2}+7x-8.

$$\frac{\frac{11}{\left(x-1\right)\left(x+8\right)}-\frac{1}{x-1}}{\frac{2}{x+8}+1}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-1\right)\left(x+8\right) and x-1 is \left(x-1\right)\left(x+8\right). Multiply \frac{1}{x-1} times \frac{x+8}{x+8}.

$$\frac{\frac{11}{\left(x-1\right)\left(x+8\right)}-\frac{x+8}{\left(x-1\right)\left(x+8\right)}}{\frac{2}{x+8}+1}$$

Since \frac{11}{\left(x-1\right)\left(x+8\right)} and \frac{x+8}{\left(x-1\right)\left(x+8\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{11-\left(x+8\right)}{\left(x-1\right)\left(x+8\right)}}{\frac{2}{x+8}+1}$$

Do the multiplications in 11-\left(x+8\right).

$$\frac{\frac{11-x-8}{\left(x-1\right)\left(x+8\right)}}{\frac{2}{x+8}+1}$$

Combine like terms in 11-x-8.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+8}{x+8}.

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

Since \frac{2}{x+8} and \frac{x+8}{x+8} have the same denominator, add them by adding their numerators.

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

Combine like terms in 2+x+8.

$$\frac{\frac{3-x}{\left(x-1\right)\left(x+8\right)}}{\frac{10+x}{x+8}}$$

Divide \frac{3-x}{\left(x-1\right)\left(x+8\right)} by \frac{10+x}{x+8} by multiplying \frac{3-x}{\left(x-1\right)\left(x+8\right)} by the reciprocal of \frac{10+x}{x+8}.

$$\frac{\left(3-x\right)\left(x+8\right)}{\left(x-1\right)\left(x+8\right)\left(10+x\right)}$$

Cancel out x+8 in both numerator and denominator.

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

Use the distributive property to multiply x-1 by x+10 and combine like terms.

$$\frac{-x+3}{x^{2}+9x-10}$$

Expand

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

Short Solution Steps

Factor x^{2}+7x-8.

$$\frac{\frac{11}{\left(x-1\right)\left(x+8\right)}-\frac{1}{x-1}}{\frac{2}{x+8}+1}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-1\right)\left(x+8\right) and x-1 is \left(x-1\right)\left(x+8\right). Multiply \frac{1}{x-1} times \frac{x+8}{x+8}.

$$\frac{\frac{11}{\left(x-1\right)\left(x+8\right)}-\frac{x+8}{\left(x-1\right)\left(x+8\right)}}{\frac{2}{x+8}+1}$$

Since \frac{11}{\left(x-1\right)\left(x+8\right)} and \frac{x+8}{\left(x-1\right)\left(x+8\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{11-\left(x+8\right)}{\left(x-1\right)\left(x+8\right)}}{\frac{2}{x+8}+1}$$

Do the multiplications in 11-\left(x+8\right).

$$\frac{\frac{11-x-8}{\left(x-1\right)\left(x+8\right)}}{\frac{2}{x+8}+1}$$

Combine like terms in 11-x-8.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x+8}{x+8}.

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

Since \frac{2}{x+8} and \frac{x+8}{x+8} have the same denominator, add them by adding their numerators.

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

Combine like terms in 2+x+8.

$$\frac{\frac{3-x}{\left(x-1\right)\left(x+8\right)}}{\frac{10+x}{x+8}}$$

Divide \frac{3-x}{\left(x-1\right)\left(x+8\right)} by \frac{10+x}{x+8} by multiplying \frac{3-x}{\left(x-1\right)\left(x+8\right)} by the reciprocal of \frac{10+x}{x+8}.

$$\frac{\left(3-x\right)\left(x+8\right)}{\left(x-1\right)\left(x+8\right)\left(10+x\right)}$$

Cancel out x+8 in both numerator and denominator.

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

Use the distributive property to multiply x-1 by x+10 and combine like terms.

$$\frac{-x+3}{x^{2}+9x-10}$$