Solve x^2-16div4x+16/3x^2

$$x ^ { 2 } - 16 \div \frac { 4 x + 16 } { 3 x ^ { 2 } }$$

Evaluate

$$\frac{\left(x-8\right)x^{2}}{x+4}$$

Short Solution Steps

Divide 16 by \frac{4x+16}{3x^{2}} by multiplying 16 by the reciprocal of \frac{4x+16}{3x^{2}}.

$$x^{2}-\frac{16\times 3x^{2}}{4x+16}$$

Multiply 16 and 3 to get 48.

$$x^{2}-\frac{48x^{2}}{4x+16}$$

Factor the expressions that are not already factored in \frac{48x^{2}}{4x+16}.

$$x^{2}-\frac{48x^{2}}{4\left(x+4\right)}$$

Cancel out 4 in both numerator and denominator.

$$x^{2}-\frac{12x^{2}}{x+4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2} times \frac{x+4}{x+4}.

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

Since \frac{x^{2}\left(x+4\right)}{x+4} and \frac{12x^{2}}{x+4} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x^{2}\left(x+4\right)-12x^{2}.

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

Combine like terms in x^{3}+4x^{2}-12x^{2}.

$$\frac{x^{3}-8x^{2}}{x+4}$$

Expand

$$\frac{x^{3}-8x^{2}}{x+4}$$

Short Solution Steps

Divide 16 by \frac{4x+16}{3x^{2}} by multiplying 16 by the reciprocal of \frac{4x+16}{3x^{2}}.

$$x^{2}-\frac{16\times 3x^{2}}{4x+16}$$

Multiply 16 and 3 to get 48.

$$x^{2}-\frac{48x^{2}}{4x+16}$$

Factor the expressions that are not already factored in \frac{48x^{2}}{4x+16}.

$$x^{2}-\frac{48x^{2}}{4\left(x+4\right)}$$

Cancel out 4 in both numerator and denominator.

$$x^{2}-\frac{12x^{2}}{x+4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2} times \frac{x+4}{x+4}.

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

Since \frac{x^{2}\left(x+4\right)}{x+4} and \frac{12x^{2}}{x+4} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x^{2}\left(x+4\right)-12x^{2}.

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

Combine like terms in x^{3}+4x^{2}-12x^{2}.

$$\frac{x^{3}-8x^{2}}{x+4}$$