Solve x+1/6+20/x-1=

$$\frac { x + 1 } { 6 } + \frac { 20 } { x - 1 } =$$

Evaluate

$$\frac{x^{2}+119}{6\left(x-1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and x-1 is 6\left(x-1\right). Multiply \frac{x+1}{6} times \frac{x-1}{x-1}. Multiply \frac{20}{x-1} times \frac{6}{6}.

$$\frac{\left(x+1\right)\left(x-1\right)}{6\left(x-1\right)}+\frac{20\times 6}{6\left(x-1\right)}$$

Since \frac{\left(x+1\right)\left(x-1\right)}{6\left(x-1\right)} and \frac{20\times 6}{6\left(x-1\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(x+1\right)\left(x-1\right)+20\times 6}{6\left(x-1\right)}$$

Do the multiplications in \left(x+1\right)\left(x-1\right)+20\times 6.

$$\frac{x^{2}-x+x-1+120}{6\left(x-1\right)}$$

Combine like terms in x^{2}-x+x-1+120.

$$\frac{x^{2}+119}{6\left(x-1\right)}$$

Expand 6\left(x-1\right).

$$\frac{x^{2}+119}{6x-6}$$

Expand

$$\frac{x^{2}+119}{6\left(x-1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and x-1 is 6\left(x-1\right). Multiply \frac{x+1}{6} times \frac{x-1}{x-1}. Multiply \frac{20}{x-1} times \frac{6}{6}.

$$\frac{\left(x+1\right)\left(x-1\right)}{6\left(x-1\right)}+\frac{20\times 6}{6\left(x-1\right)}$$

Since \frac{\left(x+1\right)\left(x-1\right)}{6\left(x-1\right)} and \frac{20\times 6}{6\left(x-1\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(x+1\right)\left(x-1\right)+20\times 6}{6\left(x-1\right)}$$

Do the multiplications in \left(x+1\right)\left(x-1\right)+20\times 6.

$$\frac{x^{2}-x+x-1+120}{6\left(x-1\right)}$$

Combine like terms in x^{2}-x+x-1+120.

$$\frac{x^{2}+119}{6\left(x-1\right)}$$

Expand 6\left(x-1\right).

$$\frac{x^{2}+119}{6x-6}$$