Pre-Algebra Examples

$\frac{4}{r} + \frac{6}{r - 1}$

Step 1

To write $\frac{4}{r}$ as a fraction with a common denominator, multiply by $\frac{r - 1}{r - 1}$ .

$\frac{4}{r} \cdot \frac{r - 1}{r - 1} + \frac{6}{r - 1}$

Step 2

To write $\frac{6}{r - 1}$ as a fraction with a common denominator, multiply by $\frac{r}{r}$ .

$\frac{4}{r} \cdot \frac{r - 1}{r - 1} + \frac{6}{r - 1} \cdot \frac{r}{r}$

Step 3

Write each expression with a common denominator of $r (r - 1)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{4}{r}$ by $\frac{r - 1}{r - 1}$ .

$\frac{4 (r - 1)}{r (r - 1)} + \frac{6}{r - 1} \cdot \frac{r}{r}$

Step 3.2

Multiply $\frac{6}{r - 1}$ by $\frac{r}{r}$ .

$\frac{4 (r - 1)}{r (r - 1)} + \frac{6 r}{(r - 1) r}$

Step 3.3

Reorder the factors of $(r - 1) r$ .

$\frac{4 (r - 1)}{r (r - 1)} + \frac{6 r}{r (r - 1)}$

Step 4

Combine the numerators over the common denominator.

$\frac{4 (r - 1) + 6 r}{r (r - 1)}$

Step 5

Simplify the numerator.

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Step 5.1

Factor $2$ out of $4 (r - 1) + 6 r$ .

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Step 5.1.1

Factor $2$ out of $4 (r - 1)$ .

$\frac{2 (2 (r - 1)) + 6 r}{r (r - 1)}$

Step 5.1.2

Factor $2$ out of $6 r$ .

$\frac{2 (2 (r - 1)) + 2 (3 r)}{r (r - 1)}$

Step 5.1.3

Factor $2$ out of $2 (2 (r - 1)) + 2 (3 r)$ .

$\frac{2 (2 (r - 1) + 3 r)}{r (r - 1)}$

Step 5.2

Apply the distributive property.

$\frac{2 (2 r + 2 \cdot - 1 + 3 r)}{r (r - 1)}$

Step 5.3

Multiply $2$ by $- 1$ .

$\frac{2 (2 r - 2 + 3 r)}{r (r - 1)}$

Step 5.4

Add $2 r$ and $3 r$ .

$\frac{2 (5 r - 2)}{r (r - 1)}$