Solve (3x - 6)/(x ^ 2 - 4) + (x ^ 2 + 6x + 4)/(x ^ 2 - x - 6) | 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

$$\frac{3x-6}{x^{2}-4}+\frac{x^{2}+6x+4}{x^{2}-x-6}$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in $\frac{3x-6}{x^{2}-4}$.

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

Cancel out $x-2$ in both numerator and denominator.

$$\frac{3}{x+2}+\frac{x^{2}+6x+4}{x^{2}-x-6}$$

Factor $x^{2}-x-6$.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x+2$ and $\left(x-3\right)\left(x+2\right)$ is $\left(x-3\right)\left(x+2\right)$. Multiply $\frac{3}{x+2}$ times $\frac{x-3}{x-3}$.

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

Since $\frac{3\left(x-3\right)}{\left(x-3\right)\left(x+2\right)}$ and $\frac{x^{2}+6x+4}{\left(x-3\right)\left(x+2\right)}$ have the same denominator, add them by adding their numerators.

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

Do the multiplications in $3\left(x-3\right)+x^{2}+6x+4$.

$$\frac{3x-9+x^{2}+6x+4}{\left(x-3\right)\left(x+2\right)}$$

Combine like terms in $3x-9+x^{2}+6x+4$.

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

Expand $\left(x-3\right)\left(x+2\right)$.

$$\frac{9x-5+x^{2}}{x^{2}-x-6}$$

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in $\frac{3x-6}{x^{2}-4}$.

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

Cancel out $x-2$ in both numerator and denominator.

$$\frac{3}{x+2}+\frac{x^{2}+6x+4}{x^{2}-x-6}$$

Factor $x^{2}-x-6$.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x+2$ and $\left(x-3\right)\left(x+2\right)$ is $\left(x-3\right)\left(x+2\right)$. Multiply $\frac{3}{x+2}$ times $\frac{x-3}{x-3}$.

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

Since $\frac{3\left(x-3\right)}{\left(x-3\right)\left(x+2\right)}$ and $\frac{x^{2}+6x+4}{\left(x-3\right)\left(x+2\right)}$ have the same denominator, add them by adding their numerators.

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

Do the multiplications in $3\left(x-3\right)+x^{2}+6x+4$.

$$\frac{3x-9+x^{2}+6x+4}{\left(x-3\right)\left(x+2\right)}$$

Combine like terms in $3x-9+x^{2}+6x+4$.

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

Expand $\left(x-3\right)\left(x+2\right)$.

$$\frac{9x-5+x^{2}}{x^{2}-x-6}$$