Solve (6x+10/x+1+x-1)+x^2-9/x+1

$$( \frac { 6 x + 10 } { x + 1 } + x - 1 ) + \frac { x ^ { 2 } - 9 } { x + 1 }$$

Evaluate

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

Short Solution Steps

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

$$\frac{6x+10}{x+1}+\frac{\left(x-1\right)\left(x+1\right)}{x+1}+\frac{x^{2}-9}{x+1}$$

Since \frac{6x+10}{x+1} and \frac{\left(x-1\right)\left(x+1\right)}{x+1} have the same denominator, add them by adding their numerators.

$$\frac{6x+10+\left(x-1\right)\left(x+1\right)}{x+1}+\frac{x^{2}-9}{x+1}$$

Do the multiplications in 6x+10+\left(x-1\right)\left(x+1\right).

$$\frac{6x+10+x^{2}+x-x-1}{x+1}+\frac{x^{2}-9}{x+1}$$

Combine like terms in 6x+10+x^{2}+x-x-1.

$$\frac{6x+9+x^{2}}{x+1}+\frac{x^{2}-9}{x+1}$$

Since \frac{6x+9+x^{2}}{x+1} and \frac{x^{2}-9}{x+1} have the same denominator, add them by adding their numerators.

$$\frac{6x+9+x^{2}+x^{2}-9}{x+1}$$

Combine like terms in 6x+9+x^{2}+x^{2}-9.

$$\frac{6x+2x^{2}}{x+1}$$

Expand

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

Short Solution Steps

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

$$\frac{6x+10}{x+1}+\frac{\left(x-1\right)\left(x+1\right)}{x+1}+\frac{x^{2}-9}{x+1}$$

Since \frac{6x+10}{x+1} and \frac{\left(x-1\right)\left(x+1\right)}{x+1} have the same denominator, add them by adding their numerators.

$$\frac{6x+10+\left(x-1\right)\left(x+1\right)}{x+1}+\frac{x^{2}-9}{x+1}$$

Do the multiplications in 6x+10+\left(x-1\right)\left(x+1\right).

$$\frac{6x+10+x^{2}+x-x-1}{x+1}+\frac{x^{2}-9}{x+1}$$

Combine like terms in 6x+10+x^{2}+x-x-1.

$$\frac{6x+9+x^{2}}{x+1}+\frac{x^{2}-9}{x+1}$$

Since \frac{6x+9+x^{2}}{x+1} and \frac{x^{2}-9}{x+1} have the same denominator, add them by adding their numerators.

$$\frac{6x+9+x^{2}+x^{2}-9}{x+1}$$

Combine like terms in 6x+9+x^{2}+x^{2}-9.

$$\frac{6x+2x^{2}}{x+1}$$