Solve x^2/9+1-2x/3

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{9}{9}.

$$\frac{x^{2}}{9}+\frac{9}{9}-\frac{2x}{3}$$

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

$$\frac{x^{2}+9}{9}-\frac{2x}{3}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9 and 3 is 9. Multiply \frac{2x}{3} times \frac{3}{3}.

$$\frac{x^{2}+9}{9}-\frac{3\times 2x}{9}$$

Since \frac{x^{2}+9}{9} and \frac{3\times 2x}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{2}+9-3\times 2x}{9}$$

Do the multiplications in x^{2}+9-3\times 2x.

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

Factor

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

Solution Steps

Factor out \frac{1}{9}.

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

Consider x^{2}+9-6x. Use the perfect square formula, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, where a=x and b=3.

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

Rewrite the complete factored expression.

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