Solve 20/x+1/frac{1{4}-7/x+1}

$$\frac{ \frac{ 20 }{ x+1 } }{ \frac{ 1 }{ 4 } - \frac{ 7 }{ x+1 } }$$

Evaluate

$$\frac{80}{x-27}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and x+1 is 4\left(x+1\right). Multiply \frac{1}{4} times \frac{x+1}{x+1}. Multiply \frac{7}{x+1} times \frac{4}{4}.

$$\frac{\frac{20}{x+1}}{\frac{x+1}{4\left(x+1\right)}-\frac{7\times 4}{4\left(x+1\right)}}$$

Since \frac{x+1}{4\left(x+1\right)} and \frac{7\times 4}{4\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{20}{x+1}}{\frac{x+1-7\times 4}{4\left(x+1\right)}}$$

Do the multiplications in x+1-7\times 4.

$$\frac{\frac{20}{x+1}}{\frac{x+1-28}{4\left(x+1\right)}}$$

Combine like terms in x+1-28.

$$\frac{\frac{20}{x+1}}{\frac{x-27}{4\left(x+1\right)}}$$

Divide \frac{20}{x+1} by \frac{x-27}{4\left(x+1\right)} by multiplying \frac{20}{x+1} by the reciprocal of \frac{x-27}{4\left(x+1\right)}.

$$\frac{20\times 4\left(x+1\right)}{\left(x+1\right)\left(x-27\right)}$$

Cancel out x+1 in both numerator and denominator.

$$\frac{4\times 20}{x-27}$$

Multiply 4 and 20 to get 80.

$$\frac{80}{x-27}$$

Differentiate w.r.t. x

$$-\frac{80}{\left(x-27\right)^{2}}$$