Simplify (n-5)/35-(n-10)/105

$\frac{n - 5}{35} - \frac{n - 10}{105}$

Step 1

To write $\frac{n - 5}{35}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{n - 5}{35} \cdot \frac{3}{3} - \frac{n - 10}{105}$

Step 2

Write each expression with a common denominator of $105$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{n - 5}{35}$ by $\frac{3}{3}$ .

$\frac{(n - 5) \cdot 3}{35 \cdot 3} - \frac{n - 10}{105}$

Multiply $35$ by $3$ .

$\frac{(n - 5) \cdot 3}{105} - \frac{n - 10}{105}$

Step 3

Combine the numerators over the common denominator.

$\frac{(n - 5) \cdot 3 - (n - 10)}{105}$

Step 4

Simplify the numerator.

Apply the distributive property.

$\frac{n \cdot 3 - 5 \cdot 3 - (n - 10)}{105}$

Move $3$ to the left of $n$ .

$\frac{3 \cdot n - 5 \cdot 3 - (n - 10)}{105}$

Multiply $- 5$ by $3$ .

$\frac{3 \cdot n - 15 - (n - 10)}{105}$

Apply the distributive property.

$\frac{3 n - 15 - n - - 10}{105}$

Multiply $- 1$ by $- 10$ .

$\frac{3 n - 15 - n + 10}{105}$

Subtract $n$ from $3 n$ .

$\frac{2 n - 15 + 10}{105}$

Add $- 15$ and $10$ .

$\frac{2 n - 5}{105}$