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

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

Evaluate

$$\frac{x}{16}-\frac{28}{9}$$

Short Solution Steps

Add -1 and 3 to get 2.

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

Calculate 2 to the power of 2 and get 4.

$$\frac{x}{4-2\left(-1+3\right)\left(-1-2\right)}+\frac{\frac{1}{3}}{-1-2}-1-2$$

Add -1 and 3 to get 2.

$$\frac{x}{4-2\times 2\left(-1-2\right)}+\frac{\frac{1}{3}}{-1-2}-1-2$$

Multiply 2 and 2 to get 4.

$$\frac{x}{4-4\left(-1-2\right)}+\frac{\frac{1}{3}}{-1-2}-1-2$$

Subtract 2 from -1 to get -3.

$$\frac{x}{4-4\left(-3\right)}+\frac{\frac{1}{3}}{-1-2}-1-2$$

Multiply 4 and -3 to get -12.

$$\frac{x}{4-\left(-12\right)}+\frac{\frac{1}{3}}{-1-2}-1-2$$

The opposite of -12 is 12.

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

Add 4 and 12 to get 16.

$$\frac{x}{16}+\frac{\frac{1}{3}}{-1-2}-1-2$$

Subtract 2 from -1 to get -3.

$$\frac{x}{16}+\frac{\frac{1}{3}}{-3}-1-2$$

Express \frac{\frac{1}{3}}{-3} as a single fraction.

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

Multiply 3 and -3 to get -9.

$$\frac{x}{16}+\frac{1}{-9}-1-2$$

Fraction \frac{1}{-9} can be rewritten as -\frac{1}{9} by extracting the negative sign.

$$\frac{x}{16}-\frac{1}{9}-1-2$$

Subtract 1 from -\frac{1}{9} to get -\frac{10}{9}.

$$\frac{x}{16}-\frac{10}{9}-2$$

Subtract 2 from -\frac{10}{9} to get -\frac{28}{9}.

$$\frac{x}{16}-\frac{28}{9}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 16 and 9 is 144. Multiply \frac{x}{16} times \frac{9}{9}. Multiply \frac{28}{9} times \frac{16}{16}.

$$\frac{9x}{144}-\frac{28\times 16}{144}$$

Since \frac{9x}{144} and \frac{28\times 16}{144} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9x-28\times 16}{144}$$

Do the multiplications in 9x-28\times 16.

$$\frac{9x-448}{144}$$

Expand

$$\frac{x}{16}-\frac{28}{9}$$

Short Solution Steps

Add -1 and 3 to get 2.

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

Calculate 2 to the power of 2 and get 4.

$$\frac{x}{4-2\left(-1+3\right)\left(-1-2\right)}+\frac{\frac{1}{3}}{-1-2}-1-2$$

Add -1 and 3 to get 2.

$$\frac{x}{4-2\times 2\left(-1-2\right)}+\frac{\frac{1}{3}}{-1-2}-1-2$$

Multiply 2 and 2 to get 4.

$$\frac{x}{4-4\left(-1-2\right)}+\frac{\frac{1}{3}}{-1-2}-1-2$$

Subtract 2 from -1 to get -3.

$$\frac{x}{4-4\left(-3\right)}+\frac{\frac{1}{3}}{-1-2}-1-2$$

Multiply 4 and -3 to get -12.

$$\frac{x}{4-\left(-12\right)}+\frac{\frac{1}{3}}{-1-2}-1-2$$

The opposite of -12 is 12.

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

Add 4 and 12 to get 16.

$$\frac{x}{16}+\frac{\frac{1}{3}}{-1-2}-1-2$$

Subtract 2 from -1 to get -3.

$$\frac{x}{16}+\frac{\frac{1}{3}}{-3}-1-2$$

Express \frac{\frac{1}{3}}{-3} as a single fraction.

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

Multiply 3 and -3 to get -9.

$$\frac{x}{16}+\frac{1}{-9}-1-2$$

Fraction \frac{1}{-9} can be rewritten as -\frac{1}{9} by extracting the negative sign.

$$\frac{x}{16}-\frac{1}{9}-1-2$$

Subtract 1 from -\frac{1}{9} to get -\frac{10}{9}.

$$\frac{x}{16}-\frac{10}{9}-2$$

Subtract 2 from -\frac{10}{9} to get -\frac{28}{9}.

$$\frac{x}{16}-\frac{28}{9}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 16 and 9 is 144. Multiply \frac{x}{16} times \frac{9}{9}. Multiply \frac{28}{9} times \frac{16}{16}.

$$\frac{9x}{144}-\frac{28\times 16}{144}$$

Since \frac{9x}{144} and \frac{28\times 16}{144} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9x-28\times 16}{144}$$

Do the multiplications in 9x-28\times 16.

$$\frac{9x-448}{144}$$