Solve 5x - 15 / ((x ^ 2 - 9)/(x + 2)) | 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

$$5x-15\div\frac{x^{2}-9}{x+2}.$$

Evaluate

$\frac{5\left(x^{3}-12x-6\right)}{x^{2}-9}$

Short Solution Steps

Divide $15$ by $\frac{x^{2}-9}{x+2}$ by multiplying $15$ by the reciprocal of $\frac{x^{2}-9}{x+2}$.

$$5x-\frac{15\left(x+2\right)}{x^{2}-9}$$

Factor $x^{2}-9$.

$$5x-\frac{15\left(x+2\right)}{\left(x-3\right)\left(x+3\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $5x$ times $\frac{\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}$.

$$\frac{5x\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}-\frac{15\left(x+2\right)}{\left(x-3\right)\left(x+3\right)}$$

Since $\frac{5x\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}$ and $\frac{15\left(x+2\right)}{\left(x-3\right)\left(x+3\right)}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{5x\left(x-3\right)\left(x+3\right)-15\left(x+2\right)}{\left(x-3\right)\left(x+3\right)}$$

Do the multiplications in $5x\left(x-3\right)\left(x+3\right)-15\left(x+2\right)$.

$$\frac{5x^{3}+15x^{2}-15x^{2}-45x-15x-30}{\left(x-3\right)\left(x+3\right)}$$

Combine like terms in $5x^{3}+15x^{2}-15x^{2}-45x-15x-30$.

$$\frac{5x^{3}-60x-30}{\left(x-3\right)\left(x+3\right)}$$

Expand $\left(x-3\right)\left(x+3\right)$.

$$\frac{5x^{3}-60x-30}{x^{2}-9}$$

Expand

$\frac{5\left(x^{3}-12x-6\right)}{x^{2}-9}$

Short Solution Steps

Divide $15$ by $\frac{x^{2}-9}{x+2}$ by multiplying $15$ by the reciprocal of $\frac{x^{2}-9}{x+2}$.

$$5x-\frac{15\left(x+2\right)}{x^{2}-9}$$

Factor $x^{2}-9$.

$$5x-\frac{15\left(x+2\right)}{\left(x-3\right)\left(x+3\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $5x$ times $\frac{\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}$.

$$\frac{5x\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}-\frac{15\left(x+2\right)}{\left(x-3\right)\left(x+3\right)}$$

Since $\frac{5x\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}$ and $\frac{15\left(x+2\right)}{\left(x-3\right)\left(x+3\right)}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{5x\left(x-3\right)\left(x+3\right)-15\left(x+2\right)}{\left(x-3\right)\left(x+3\right)}$$

Do the multiplications in $5x\left(x-3\right)\left(x+3\right)-15\left(x+2\right)$.

$$\frac{5x^{3}+15x^{2}-15x^{2}-45x-15x-30}{\left(x-3\right)\left(x+3\right)}$$

Combine like terms in $5x^{3}+15x^{2}-15x^{2}-45x-15x-30$.

$$\frac{5x^{3}-60x-30}{\left(x-3\right)\left(x+3\right)}$$

Expand $\left(x-3\right)\left(x+3\right)$.

$$\frac{5x^{3}-60x-30}{x^{2}-9}$$