Solve x^2-16/x-9divx-4

$$\frac{ { x }^{ 2 } -16 }{ x-9 } \div x-4$$

Evaluate

$$\frac{-3x^{2}+36x-16}{x\left(x-9\right)}$$

Short Solution Steps

Express \frac{\frac{x^{2}-16}{x-9}}{x} as a single fraction.

$$\frac{x^{2}-16}{\left(x-9\right)x}-4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{\left(x-9\right)x}{\left(x-9\right)x}.

$$\frac{x^{2}-16}{\left(x-9\right)x}-\frac{4\left(x-9\right)x}{\left(x-9\right)x}$$

Since \frac{x^{2}-16}{\left(x-9\right)x} and \frac{4\left(x-9\right)x}{\left(x-9\right)x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{2}-16-4\left(x-9\right)x}{\left(x-9\right)x}$$

Do the multiplications in x^{2}-16-4\left(x-9\right)x.

$$\frac{x^{2}-16-4x^{2}+36x}{\left(x-9\right)x}$$

Combine like terms in x^{2}-16-4x^{2}+36x.

$$\frac{-3x^{2}-16+36x}{\left(x-9\right)x}$$

Expand \left(x-9\right)x.

$$\frac{-3x^{2}-16+36x}{x^{2}-9x}$$

Expand

$$\frac{-3x^{2}+36x-16}{x\left(x-9\right)}$$

Short Solution Steps

Express \frac{\frac{x^{2}-16}{x-9}}{x} as a single fraction.

$$\frac{x^{2}-16}{\left(x-9\right)x}-4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{\left(x-9\right)x}{\left(x-9\right)x}.

$$\frac{x^{2}-16}{\left(x-9\right)x}-\frac{4\left(x-9\right)x}{\left(x-9\right)x}$$

Since \frac{x^{2}-16}{\left(x-9\right)x} and \frac{4\left(x-9\right)x}{\left(x-9\right)x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{2}-16-4\left(x-9\right)x}{\left(x-9\right)x}$$

Do the multiplications in x^{2}-16-4\left(x-9\right)x.

$$\frac{x^{2}-16-4x^{2}+36x}{\left(x-9\right)x}$$

Combine like terms in x^{2}-16-4x^{2}+36x.

$$\frac{-3x^{2}-16+36x}{\left(x-9\right)x}$$

Expand \left(x-9\right)x.

$$\frac{-3x^{2}-16+36x}{x^{2}-9x}$$