Evaluate (x+h)/((x+h)^2+1)

$\frac{(x + h)}{{(x + h)}^{2} + 1}$

Step 1

Rewrite ${(x + h)}^{2}$ as $(x + h) (x + h)$ .

$\frac{x + h}{(x + h) (x + h) + 1}$

Step 2

Expand $(x + h) (x + h)$ using the FOIL Method.

Apply the distributive property.

$\frac{x + h}{x (x + h) + h (x + h) + 1}$

Apply the distributive property.

$\frac{x + h}{x \cdot x + x h + h (x + h) + 1}$

Apply the distributive property.

$\frac{x + h}{x \cdot x + x h + h x + h \cdot h + 1}$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$\frac{x + h}{x^{2} + x h + h x + h \cdot h + 1}$

Multiply $h$ by $h$ .

$\frac{x + h}{x^{2} + x h + h x + h^{2} + 1}$

Add $x h$ and $h x$ .

Reorder $x$ and $h$ .

$\frac{x + h}{x^{2} + h x + h x + h^{2} + 1}$

Add $h x$ and $h x$ .

$\frac{x + h}{x^{2} + 2 h x + h^{2} + 1}$