Basic Math Examples

$\frac{w + 10}{w + 1} + \frac{w - 7}{w - 1}$

Step 1

To write $\frac{w + 10}{w + 1}$ as a fraction with a common denominator, multiply by $\frac{w - 1}{w - 1}$ .

$\frac{w + 10}{w + 1} \cdot \frac{w - 1}{w - 1} + \frac{w - 7}{w - 1}$

Step 2

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

$\frac{w + 10}{w + 1} \cdot \frac{w - 1}{w - 1} + \frac{w - 7}{w - 1} \cdot \frac{w + 1}{w + 1}$

Step 3

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

Tap for more steps...

Step 3.1

Multiply $\frac{w + 10}{w + 1}$ by $\frac{w - 1}{w - 1}$ .

$\frac{(w + 10) (w - 1)}{(w + 1) (w - 1)} + \frac{w - 7}{w - 1} \cdot \frac{w + 1}{w + 1}$

Step 3.2

Multiply $\frac{w - 7}{w - 1}$ by $\frac{w + 1}{w + 1}$ .

$\frac{(w + 10) (w - 1)}{(w + 1) (w - 1)} + \frac{(w - 7) (w + 1)}{(w - 1) (w + 1)}$

Step 3.3

Reorder the factors of $(w - 1) (w + 1)$ .

$\frac{(w + 10) (w - 1)}{(w + 1) (w - 1)} + \frac{(w - 7) (w + 1)}{(w + 1) (w - 1)}$

Step 4

Combine the numerators over the common denominator.

$\frac{(w + 10) (w - 1) + (w - 7) (w + 1)}{(w + 1) (w - 1)}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Expand $(w + 10) (w - 1)$ using the FOIL Method.

Tap for more steps...

Step 5.1.1

Apply the distributive property.

$\frac{w (w - 1) + 10 (w - 1) + (w - 7) (w + 1)}{(w + 1) (w - 1)}$

Step 5.1.2

Apply the distributive property.

$\frac{w \cdot w + w \cdot - 1 + 10 (w - 1) + (w - 7) (w + 1)}{(w + 1) (w - 1)}$

Step 5.1.3

Apply the distributive property.

$\frac{w \cdot w + w \cdot - 1 + 10 w + 10 \cdot - 1 + (w - 7) (w + 1)}{(w + 1) (w - 1)}$

Step 5.2

Simplify and combine like terms.

Tap for more steps...

Step 5.2.1

Simplify each term.

Tap for more steps...

Step 5.2.1.1

Multiply $w$ by $w$ .

$\frac{w^{2} + w \cdot - 1 + 10 w + 10 \cdot - 1 + (w - 7) (w + 1)}{(w + 1) (w - 1)}$

Step 5.2.1.2

Move $- 1$ to the left of $w$ .

$\frac{w^{2} - 1 \cdot w + 10 w + 10 \cdot - 1 + (w - 7) (w + 1)}{(w + 1) (w - 1)}$

Step 5.2.1.3

Rewrite $- 1 w$ as $- w$ .

$\frac{w^{2} - w + 10 w + 10 \cdot - 1 + (w - 7) (w + 1)}{(w + 1) (w - 1)}$

Step 5.2.1.4

Multiply $10$ by $- 1$ .

$\frac{w^{2} - w + 10 w - 10 + (w - 7) (w + 1)}{(w + 1) (w - 1)}$

Step 5.2.2

Add $- w$ and $10 w$ .

$\frac{w^{2} + 9 w - 10 + (w - 7) (w + 1)}{(w + 1) (w - 1)}$

Step 5.3

Expand $(w - 7) (w + 1)$ using the FOIL Method.

Tap for more steps...

Step 5.3.1

Apply the distributive property.

$\frac{w^{2} + 9 w - 10 + w (w + 1) - 7 (w + 1)}{(w + 1) (w - 1)}$

Step 5.3.2

Apply the distributive property.

$\frac{w^{2} + 9 w - 10 + w \cdot w + w \cdot 1 - 7 (w + 1)}{(w + 1) (w - 1)}$

Step 5.3.3

Apply the distributive property.

$\frac{w^{2} + 9 w - 10 + w \cdot w + w \cdot 1 - 7 w - 7 \cdot 1}{(w + 1) (w - 1)}$

Step 5.4

Simplify and combine like terms.

Tap for more steps...

Step 5.4.1

Simplify each term.

Tap for more steps...

Step 5.4.1.1

Multiply $w$ by $w$ .

$\frac{w^{2} + 9 w - 10 + w^{2} + w \cdot 1 - 7 w - 7 \cdot 1}{(w + 1) (w - 1)}$

Step 5.4.1.2

Multiply $w$ by $1$ .

$\frac{w^{2} + 9 w - 10 + w^{2} + w - 7 w - 7 \cdot 1}{(w + 1) (w - 1)}$

Step 5.4.1.3

Multiply $- 7$ by $1$ .

$\frac{w^{2} + 9 w - 10 + w^{2} + w - 7 w - 7}{(w + 1) (w - 1)}$

Step 5.4.2

Subtract $7 w$ from $w$ .

$\frac{w^{2} + 9 w - 10 + w^{2} - 6 w - 7}{(w + 1) (w - 1)}$

Step 5.5

Add $w^{2}$ and $w^{2}$ .

$\frac{2 w^{2} + 9 w - 10 - 6 w - 7}{(w + 1) (w - 1)}$

Step 5.6

Subtract $6 w$ from $9 w$ .

$\frac{2 w^{2} + 3 w - 10 - 7}{(w + 1) (w - 1)}$

Step 5.7

Subtract $7$ from $- 10$ .

$\frac{2 w^{2} + 3 w - 17}{(w + 1) (w - 1)}$