Solve (x-1):3-5:(x+1)

$$( x - 1 ) : 3 - 5 : ( x + 1 )$$

Evaluate

$$\frac{x^{2}-16}{3\left(x+1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and x+1 is 3\left(x+1\right). Multiply \frac{x-1}{3} times \frac{x+1}{x+1}. Multiply \frac{5}{x+1} times \frac{3}{3}.

$$\frac{\left(x-1\right)\left(x+1\right)}{3\left(x+1\right)}-\frac{5\times 3}{3\left(x+1\right)}$$

Since \frac{\left(x-1\right)\left(x+1\right)}{3\left(x+1\right)} and \frac{5\times 3}{3\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(x-1\right)\left(x+1\right)-5\times 3}{3\left(x+1\right)}$$

Do the multiplications in \left(x-1\right)\left(x+1\right)-5\times 3.

$$\frac{x^{2}+x-x-1-15}{3\left(x+1\right)}$$

Combine like terms in x^{2}+x-x-1-15.

$$\frac{x^{2}-16}{3\left(x+1\right)}$$

Expand 3\left(x+1\right).

$$\frac{x^{2}-16}{3x+3}$$

Expand

$$\frac{x^{2}-16}{3\left(x+1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and x+1 is 3\left(x+1\right). Multiply \frac{x-1}{3} times \frac{x+1}{x+1}. Multiply \frac{5}{x+1} times \frac{3}{3}.

$$\frac{\left(x-1\right)\left(x+1\right)}{3\left(x+1\right)}-\frac{5\times 3}{3\left(x+1\right)}$$

Since \frac{\left(x-1\right)\left(x+1\right)}{3\left(x+1\right)} and \frac{5\times 3}{3\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(x-1\right)\left(x+1\right)-5\times 3}{3\left(x+1\right)}$$

Do the multiplications in \left(x-1\right)\left(x+1\right)-5\times 3.

$$\frac{x^{2}+x-x-1-15}{3\left(x+1\right)}$$

Combine like terms in x^{2}+x-x-1-15.

$$\frac{x^{2}-16}{3\left(x+1\right)}$$

Expand 3\left(x+1\right).

$$\frac{x^{2}-16}{3x+3}$$