Solve (x+1)^2/6+(x-1)^2/12-x^2-1/4=

$$\frac { ( x + 1 ) ^ { 2 } } { 6 } + \frac { ( x - 1 ) ^ { 2 } } { 12 } - \frac { x ^ { 2 } - 1 } { 4 } =$$

Evaluate

$$\frac{x+3}{6}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 12 is 12. Multiply \frac{\left(x+1\right)^{2}}{6} times \frac{2}{2}.

$$\frac{2\left(x+1\right)^{2}}{12}+\frac{\left(x-1\right)^{2}}{12}-\frac{x^{2}-1}{4}$$

Since \frac{2\left(x+1\right)^{2}}{12} and \frac{\left(x-1\right)^{2}}{12} have the same denominator, add them by adding their numerators.

$$\frac{2\left(x+1\right)^{2}+\left(x-1\right)^{2}}{12}-\frac{x^{2}-1}{4}$$

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

$$\frac{2x^{2}+4x+2+x^{2}-2x+1}{12}-\frac{x^{2}-1}{4}$$

Combine like terms in 2x^{2}+4x+2+x^{2}-2x+1.

$$\frac{3x^{2}+2x+3}{12}-\frac{x^{2}-1}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 12 and 4 is 12. Multiply \frac{x^{2}-1}{4} times \frac{3}{3}.

$$\frac{3x^{2}+2x+3}{12}-\frac{3\left(x^{2}-1\right)}{12}$$

Since \frac{3x^{2}+2x+3}{12} and \frac{3\left(x^{2}-1\right)}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3x^{2}+2x+3-3\left(x^{2}-1\right)}{12}$$

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

$$\frac{3x^{2}+2x+3-3x^{2}+3}{12}$$

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

$$\frac{2x+6}{12}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 12 is 12. Multiply \frac{\left(x+1\right)^{2}}{6} times \frac{2}{2}.

$$\frac{2\left(x+1\right)^{2}}{12}+\frac{\left(x-1\right)^{2}}{12}-\frac{x^{2}-1}{4}$$

Since \frac{2\left(x+1\right)^{2}}{12} and \frac{\left(x-1\right)^{2}}{12} have the same denominator, add them by adding their numerators.

$$\frac{2\left(x+1\right)^{2}+\left(x-1\right)^{2}}{12}-\frac{x^{2}-1}{4}$$

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

$$\frac{2x^{2}+4x+2+x^{2}-2x+1}{12}-\frac{x^{2}-1}{4}$$

Combine like terms in 2x^{2}+4x+2+x^{2}-2x+1.

$$\frac{3x^{2}+2x+3}{12}-\frac{x^{2}-1}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 12 and 4 is 12. Multiply \frac{x^{2}-1}{4} times \frac{3}{3}.

$$\frac{3x^{2}+2x+3}{12}-\frac{3\left(x^{2}-1\right)}{12}$$

Since \frac{3x^{2}+2x+3}{12} and \frac{3\left(x^{2}-1\right)}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3x^{2}+2x+3-3\left(x^{2}-1\right)}{12}$$

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

$$\frac{3x^{2}+2x+3-3x^{2}+3}{12}$$

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

$$\frac{2x+6}{12}$$