Solve 9-x^2div3x-9

$$9 - x ^ { 2 } \div 3 x - 9$$

Evaluate

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

Short Solution Steps

Express \frac{x^{2}}{3}x as a single fraction.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{3}{3}.

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

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

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

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

$$\frac{27-x^{3}}{3}-9$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 9 times \frac{3}{3}.

$$\frac{27-x^{3}}{3}-\frac{9\times 3}{3}$$

Since \frac{27-x^{3}}{3} and \frac{9\times 3}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{27-x^{3}-9\times 3}{3}$$

Do the multiplications in 27-x^{3}-9\times 3.

$$\frac{27-x^{3}-27}{3}$$

Combine like terms in 27-x^{3}-27.

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

Differentiate w.r.t. x

$$-x^{2}$$