Solve 3x^2/x^2-1+3x/1+x

$$\frac { 3 x ^ { 2 } } { x ^ { 2 } - 1 } + \frac { 3 x } { 1 + x }$$

Evaluate

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

Short Solution Steps

Factor x^{2}-1.

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

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

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

Since \frac{3x^{2}}{\left(x-1\right)\left(x+1\right)} and \frac{3x\left(x-1\right)}{\left(x-1\right)\left(x+1\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 3x^{2}+3x\left(x-1\right).

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

Combine like terms in 3x^{2}+3x^{2}-3x.

$$\frac{6x^{2}-3x}{\left(x-1\right)\left(x+1\right)}$$

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

$$\frac{6x^{2}-3x}{x^{2}-1}$$

Factor

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