Pre-Algebra Examples

$y - \frac{y - 1}{y + 1}$

Step 1

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

$\frac{y (y + 1)}{y + 1} - \frac{y - 1}{y + 1}$

Step 2

Combine the numerators over the common denominator.

$\frac{y (y + 1) - (y - 1)}{y + 1}$

Step 3

Simplify the numerator.

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Step 3.1

Apply the distributive property.

$\frac{y \cdot y + y \cdot 1 - (y - 1)}{y + 1}$

Step 3.2

Multiply $y$ by $y$ .

$\frac{y^{2} + y \cdot 1 - (y - 1)}{y + 1}$

Step 3.3

Multiply $y$ by $1$ .

$\frac{y^{2} + y - (y - 1)}{y + 1}$

Step 3.4

Apply the distributive property.

$\frac{y^{2} + y - y - - 1}{y + 1}$

Step 3.5

Multiply $- 1$ by $- 1$ .

$\frac{y^{2} + y - y + 1}{y + 1}$

Step 3.6

Subtract $y$ from $y$ .

$\frac{y^{2} + 0 + 1}{y + 1}$

Step 3.7

Add $y^{2}$ and $0$ .

$\frac{y^{2} + 1}{y + 1}$