Solve 2x^2-5x-3*3/x-3

$$2 x ^ { 2 } - 5 x - 3 \cdot \frac { 3 } { x - 3 }$$

Evaluate

$$\frac{2x^{3}-11x^{2}+15x-9}{x-3}$$

Short Solution Steps

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

$$2x^{2}-5x-\frac{3\times 3}{x-3}$$

Multiply 3 and 3 to get 9.

$$2x^{2}-5x-\frac{9}{x-3}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x^{2}-5x times \frac{x-3}{x-3}.

$$\frac{\left(2x^{2}-5x\right)\left(x-3\right)}{x-3}-\frac{9}{x-3}$$

Since \frac{\left(2x^{2}-5x\right)\left(x-3\right)}{x-3} and \frac{9}{x-3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(2x^{2}-5x\right)\left(x-3\right)-9}{x-3}$$

Do the multiplications in \left(2x^{2}-5x\right)\left(x-3\right)-9.

$$\frac{2x^{3}-6x^{2}-5x^{2}+15x-9}{x-3}$$

Combine like terms in 2x^{3}-6x^{2}-5x^{2}+15x-9.

$$\frac{2x^{3}-11x^{2}+15x-9}{x-3}$$

Differentiate w.r.t. x

$$\frac{4x^{3}-29x^{2}+66x-36}{\left(x-3\right)^{2}}$$