Solve 2/1+3-1/3/frac{x^2{3}-3}

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

Evaluate

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

Short Solution Steps

Add 1 and 3 to get 4.

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

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

Subtract \frac{1}{3} from \frac{1}{2} to get \frac{1}{6}.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{3}{3}.

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

Since \frac{x^{2}}{3} and \frac{3\times 3}{3} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x^{2}-3\times 3.

$$\frac{\frac{1}{6}}{\frac{x^{2}-9}{3}}$$

Divide \frac{1}{6} by \frac{x^{2}-9}{3} by multiplying \frac{1}{6} by the reciprocal of \frac{x^{2}-9}{3}.

$$\frac{3}{6\left(x^{2}-9\right)}$$

Use the distributive property to multiply 6 by x^{2}-9.

$$\frac{3}{6x^{2}-54}$$

Expand

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

Short Solution Steps

Add 1 and 3 to get 4.

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

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

Subtract \frac{1}{3} from \frac{1}{2} to get \frac{1}{6}.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{3}{3}.

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

Since \frac{x^{2}}{3} and \frac{3\times 3}{3} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x^{2}-3\times 3.

$$\frac{\frac{1}{6}}{\frac{x^{2}-9}{3}}$$

Divide \frac{1}{6} by \frac{x^{2}-9}{3} by multiplying \frac{1}{6} by the reciprocal of \frac{x^{2}-9}{3}.

$$\frac{3}{6\left(x^{2}-9\right)}$$

Use the distributive property to multiply 6 by x^{2}-9.

$$\frac{3}{6x^{2}-54}$$