Precalculus Examples

$\frac{1}{4} \cdot (\ln (x + 3) \ln (x - 1)) - \frac{1}{2} \cdot \ln (x + 2)$

Step 1

Simplify each term.

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Step 1.1

Multiply $\frac{1}{4} (\ln (x + 3) \ln (x - 1))$ .

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Step 1.1.1

Combine $\ln (x + 3)$ and $\frac{1}{4}$ .

$\frac{\ln (x + 3)}{4} \ln (x - 1) - \frac{1}{2} \cdot \ln (x + 2)$

Step 1.1.2

Combine $\frac{\ln (x + 3)}{4}$ and $\ln (x - 1)$ .

$\frac{\ln (x + 3) \ln (x - 1)}{4} - \frac{1}{2} \cdot \ln (x + 2)$

Step 1.2

Combine $\ln (x + 2)$ and $\frac{1}{2}$ .

$\frac{\ln (x + 3) \ln (x - 1)}{4} - \frac{\ln (x + 2)}{2}$

Step 2

To write $- \frac{\ln (x + 2)}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{\ln (x + 3) \ln (x - 1)}{4} - \frac{\ln (x + 2)}{2} \cdot \frac{2}{2}$

Step 3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{\ln (x + 2)}{2}$ by $\frac{2}{2}$ .

$\frac{\ln (x + 3) \ln (x - 1)}{4} - \frac{\ln (x + 2) \cdot 2}{2 \cdot 2}$

Step 3.2

Multiply $2$ by $2$ .

$\frac{\ln (x + 3) \ln (x - 1)}{4} - \frac{\ln (x + 2) \cdot 2}{4}$

Step 4

Combine the numerators over the common denominator.

$\frac{\ln (x + 3) \ln (x - 1) - \ln (x + 2) \cdot 2}{4}$

Step 5

Multiply $2$ by $- 1$ .

$\frac{\ln (x + 3) \ln (x - 1) - 2 \ln (x + 2)}{4}$