Basic Math Examples

$r - \frac{r}{r + \frac{1}{7}}$

Step 1

Simplify each term.

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Step 1.1

Simplify the denominator.

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Step 1.1.1

To write $r$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$r - \frac{r}{r \cdot \frac{7}{7} + \frac{1}{7}}$

Step 1.1.2

Combine $r$ and $\frac{7}{7}$ .

$r - \frac{r}{\frac{r \cdot 7}{7} + \frac{1}{7}}$

Step 1.1.3

Combine the numerators over the common denominator.

$r - \frac{r}{\frac{r \cdot 7 + 1}{7}}$

Step 1.1.4

Move $7$ to the left of $r$ .

$r - \frac{r}{\frac{7 r + 1}{7}}$

Step 1.2

Multiply the numerator by the reciprocal of the denominator.

$r - (r \frac{7}{7 r + 1})$

Step 1.3

Combine $r$ and $\frac{7}{7 r + 1}$ .

$r - \frac{r \cdot 7}{7 r + 1}$

Step 1.4

Move $7$ to the left of $r$ .

$r - \frac{7 r}{7 r + 1}$

Step 2

To write $r$ as a fraction with a common denominator, multiply by $\frac{7 r + 1}{7 r + 1}$ .

$\frac{r (7 r + 1)}{7 r + 1} - \frac{7 r}{7 r + 1}$

Step 3

Combine the numerators over the common denominator.

$\frac{r (7 r + 1) - 7 r}{7 r + 1}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $r$ out of $r (7 r + 1) - 7 r$ .

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Step 4.1.1

Factor $r$ out of $- 7 r$ .

$\frac{r (7 r + 1) + r \cdot - 7}{7 r + 1}$

Step 4.1.2

Factor $r$ out of $r (7 r + 1) + r \cdot - 7$ .

$\frac{r (7 r + 1 - 7)}{7 r + 1}$

Step 4.2

Subtract $7$ from $1$ .

$\frac{r (7 r - 6)}{7 r + 1}$