Solve (x ^ 2 + 12x + 36)/(x ^ 2 - 16) / ((3x + 18)/(2x ^ 2 + 8x)) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$\frac{x^{2}+12x+36}{x^{2}-16}\div\frac{3x+18}{2x^{2}+8x}$$

Evaluate

$\frac{2x\left(x+6\right)}{3\left(x-4\right)}$

Short Solution Steps

Divide $\frac{x^{2}+12x+36}{x^{2}-16}$ by $\frac{3x+18}{2x^{2}+8x}$ by multiplying $\frac{x^{2}+12x+36}{x^{2}-16}$ by the reciprocal of $\frac{3x+18}{2x^{2}+8x}$.

$$\frac{\left(x^{2}+12x+36\right)\left(2x^{2}+8x\right)}{\left(x^{2}-16\right)\left(3x+18\right)}$$

Factor the expressions that are not already factored.

$$\frac{2x\left(x+4\right)\left(x+6\right)^{2}}{3\left(x-4\right)\left(x+4\right)\left(x+6\right)}$$

Cancel out $\left(x+4\right)\left(x+6\right)$ in both numerator and denominator.

$$\frac{2x\left(x+6\right)}{3\left(x-4\right)}$$

Expand the expression.

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

Expand

$\frac{2\left(x^{2}+6x\right)}{3\left(x-4\right)}$

Short Solution Steps

Divide $\frac{x^{2}+12x+36}{x^{2}-16}$ by $\frac{3x+18}{2x^{2}+8x}$ by multiplying $\frac{x^{2}+12x+36}{x^{2}-16}$ by the reciprocal of $\frac{3x+18}{2x^{2}+8x}$.

$$\frac{\left(x^{2}+12x+36\right)\left(2x^{2}+8x\right)}{\left(x^{2}-16\right)\left(3x+18\right)}$$

Factor the expressions that are not already factored.

$$\frac{2x\left(x+4\right)\left(x+6\right)^{2}}{3\left(x-4\right)\left(x+4\right)\left(x+6\right)}$$

Cancel out $\left(x+4\right)\left(x+6\right)$ in both numerator and denominator.

$$\frac{2x\left(x+6\right)}{3\left(x-4\right)}$$

Expand the expression.

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