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Evaluate (-12^3-48x^2)÷(-4xx)

$(- 12^{3} - 48 x^{2}) \div (- 4 x \cdot x)$

Step 1

Rewrite the division as a fraction.

$\frac{- 12^{3} - 48 x^{2}}{- 4 x \cdot x}$

Step 2

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$\frac{- 12^{3} - 48 x^{2}}{- 4 (x \cdot x)}$

Multiply $x$ by $x$ .

$\frac{- 12^{3} - 48 x^{2}}{- 4 x^{2}}$

$\frac{- 12^{3} - 48 x^{2}}{- 4 x^{2}}$

Step 3

Simplify the numerator.

Raise $12$ to the power of $3$ .

$\frac{- 1 \cdot 1728 - 48 x^{2}}{- 4 x^{2}}$

Multiply $- 1$ by $1728$ .

$\frac{- 1728 - 48 x^{2}}{- 4 x^{2}}$

Factor $48$ out of $- 1728 - 48 x^{2}$ .

Factor $48$ out of $- 1728$ .

$\frac{48 (- 36) - 48 x^{2}}{- 4 x^{2}}$

Factor $48$ out of $- 48 x^{2}$ .

$\frac{48 (- 36) + 48 (- x^{2})}{- 4 x^{2}}$

Factor $48$ out of $48 (- 36) + 48 (- x^{2})$ .

$\frac{48 (- 36 - x^{2})}{- 4 x^{2}}$

$\frac{48 (- 36 - x^{2})}{- 4 x^{2}}$

$\frac{48 (- 36 - x^{2})}{- 4 x^{2}}$

Step 4

Simplify terms.

Cancel the common factor of $48$ and $- 4$ .

Factor $4$ out of $48 (- 36 - x^{2})$ .

$\frac{4 (12 (- 36 - x^{2}))}{- 4 x^{2}}$

Cancel the common factors.

Factor $4$ out of $- 4 x^{2}$ .

$\frac{4 (12 (- 36 - x^{2}))}{4 (- x^{2})}$

Cancel the common factor.

$\frac{4 (12 (- 36 - x^{2}))}{4 (- x^{2})}$

Rewrite the expression.

$\frac{12 (- 36 - x^{2})}{- x^{2}}$

$\frac{12 (- 36 - x^{2})}{- x^{2}}$

$\frac{12 (- 36 - x^{2})}{- x^{2}}$

Move the negative in front of the fraction.

$- \frac{12 (- 36 - x^{2})}{x^{2}}$

Rewrite $- 36$ as $- 1 (36)$ .

$- \frac{12 (- 1 (36) - x^{2})}{x^{2}}$

Factor $- 1$ out of $- x^{2}$ .

$- \frac{12 (- 1 (36) - (x^{2}))}{x^{2}}$

Factor $- 1$ out of $- 1 (36) - (x^{2})$ .

$- \frac{12 (- 1 (36 + x^{2}))}{x^{2}}$

Simplify the expression.

Move the negative in front of the fraction.

$- - \frac{12 (36 + x^{2})}{x^{2}}$

Multiply $- 1$ by $- 1$ .

$1 \frac{12 (36 + x^{2})}{x^{2}}$

Multiply $\frac{12 (36 + x^{2})}{x^{2}}$ by $1$ .

$\frac{12 (36 + x^{2})}{x^{2}}$

$\frac{12 (36 + x^{2})}{x^{2}}$

$\frac{12 (36 + x^{2})}{x^{2}}$

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