Simplify (a+b)/c+c/(a+b)

$\frac{a + b}{c} + \frac{c}{a + b}$

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

$\frac{a + b}{c} \cdot \frac{a + b}{a + b} + \frac{c}{a + b}$

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

$\frac{a + b}{c} \cdot \frac{a + b}{a + b} + \frac{c}{a + b} \cdot \frac{c}{c}$

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

Multiply $\frac{a + b}{c}$ by $\frac{a + b}{a + b}$ .

$\frac{(a + b) (a + b)}{c (a + b)} + \frac{c}{a + b} \cdot \frac{c}{c}$

Multiply $\frac{c}{a + b}$ by $\frac{c}{c}$ .

$\frac{(a + b) (a + b)}{c (a + b)} + \frac{c \cdot c}{(a + b) c}$

Reorder the factors of $(a + b) c$ .

$\frac{(a + b) (a + b)}{c (a + b)} + \frac{c \cdot c}{c (a + b)}$

Combine the numerators over the common denominator.

$\frac{(a + b) (a + b) + c \cdot c}{c (a + b)}$

Simplify the numerator.

Expand $(a + b) (a + b)$ using the FOIL Method.

Apply the distributive property.

$\frac{a (a + b) + b (a + b) + c \cdot c}{c (a + b)}$

Apply the distributive property.

$\frac{a \cdot a + a b + b (a + b) + c \cdot c}{c (a + b)}$

Apply the distributive property.

$\frac{a \cdot a + a b + b a + b \cdot b + c \cdot c}{c (a + b)}$

Simplify and combine like terms.

Simplify each term.

Multiply $a$ by $a$ .

$\frac{a^{2} + a b + b a + b \cdot b + c \cdot c}{c (a + b)}$

Multiply $b$ by $b$ .

$\frac{a^{2} + a b + b a + b^{2} + c \cdot c}{c (a + b)}$

Add $a b$ and $b a$ .

Reorder $b$ and $a$ .

$\frac{a^{2} + a b + a b + b^{2} + c \cdot c}{c (a + b)}$

Add $a b$ and $a b$ .

$\frac{a^{2} + 2 a b + b^{2} + c \cdot c}{c (a + b)}$

Multiply $c$ by $c$ .

$\frac{a^{2} + 2 a b + b^{2} + c^{2}}{c (a + b)}$