Simplify (h^2i-3h^2i^2)/(hi)+(3h^2+9h^2i)/(3h)

$\frac{h^{2} i - 3 h^{2} i^{2}}{h i} + \frac{3 h^{2} + 9 h^{2} i}{3 h}$

Simplify each term.

Factor $h^{2} i$ out of $h^{2} i - 3 h^{2} i^{2}$ .

Factor $h^{2} i$ out of $h^{2} i$ .

$\frac{h^{2} i (1) - 3 h^{2} i^{2}}{h i} + \frac{3 h^{2} + 9 h^{2} i}{3 h}$

Factor $h^{2} i$ out of $- 3 h^{2} i^{2}$ .

$\frac{h^{2} i (1) + h^{2} i (- 3 i)}{h i} + \frac{3 h^{2} + 9 h^{2} i}{3 h}$

Factor $h^{2} i$ out of $h^{2} i (1) + h^{2} i (- 3 i)$ .

$\frac{h^{2} i (1 - 3 i)}{h i} + \frac{3 h^{2} + 9 h^{2} i}{3 h}$

Cancel the common factor of $h^{2}$ and $h$ .

Factor $h$ out of $h^{2} i (1 - 3 i)$ .

$\frac{h (h i (1 - 3 i))}{h i} + \frac{3 h^{2} + 9 h^{2} i}{3 h}$

Cancel the common factors.

Factor $h$ out of $h i$ .

$\frac{h (h i (1 - 3 i))}{h (i)} + \frac{3 h^{2} + 9 h^{2} i}{3 h}$

Cancel the common factor.

$\frac{h (h i (1 - 3 i))}{h i} + \frac{3 h^{2} + 9 h^{2} i}{3 h}$

Rewrite the expression.

$\frac{h i (1 - 3 i)}{i} + \frac{3 h^{2} + 9 h^{2} i}{3 h}$

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{h i (1 - 3 i)}{i} + \frac{3 h^{2} + 9 h^{2} i}{3 h}$

Divide $h (1 - 3 i)$ by $1$ .

$h (1 - 3 i) + \frac{3 h^{2} + 9 h^{2} i}{3 h}$

Apply the distributive property.

$h \cdot 1 + h (- 3 i) + \frac{3 h^{2} + 9 h^{2} i}{3 h}$

Multiply $h$ by $1$ .

$h + h (- 3 i) + \frac{3 h^{2} + 9 h^{2} i}{3 h}$

Factor $3 h^{2}$ out of $3 h^{2} + 9 h^{2} i$ .

Factor $3 h^{2}$ out of $3 h^{2}$ .

$h + h (- 3 i) + \frac{3 h^{2} (1) + 9 h^{2} i}{3 h}$

Factor $3 h^{2}$ out of $9 h^{2} i$ .

$h + h (- 3 i) + \frac{3 h^{2} (1) + 3 h^{2} (3 i)}{3 h}$

Factor $3 h^{2}$ out of $3 h^{2} (1) + 3 h^{2} (3 i)$ .

$h + h (- 3 i) + \frac{3 h^{2} (1 + 3 i)}{3 h}$

Cancel the common factor of $3$ .

Cancel the common factor.

$h + h (- 3 i) + \frac{3 h^{2} (1 + 3 i)}{3 h}$

Rewrite the expression.

$h + h (- 3 i) + \frac{h^{2} (1 + 3 i)}{h}$

Cancel the common factor of $h^{2}$ and $h$ .

Factor $h$ out of $h^{2} (1 + 3 i)$ .

$h + h (- 3 i) + \frac{h (h (1 + 3 i))}{h}$

Cancel the common factors.

Raise $h$ to the power of $1$ .

$h + h (- 3 i) + \frac{h (h (1 + 3 i))}{h^{1}}$

Factor $h$ out of $h^{1}$ .

$h + h (- 3 i) + \frac{h (h (1 + 3 i))}{h \cdot 1}$

Cancel the common factor.

$h + h (- 3 i) + \frac{h (h (1 + 3 i))}{h \cdot 1}$

Rewrite the expression.

$h + h (- 3 i) + \frac{h (1 + 3 i)}{1}$

Divide $h (1 + 3 i)$ by $1$ .

$h + h (- 3 i) + h (1 + 3 i)$

Apply the distributive property.

$h + h (- 3 i) + h \cdot 1 + h (3 i)$

Multiply $h$ by $1$ .

$h + h (- 3 i) + h + h (3 i)$

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

$h + h (- 3 i) + h + 3 h i$

Simplify by adding terms.

Combine the opposite terms in $h + h (- 3 i) + h + 3 h i$ .

Reorder the factors in the terms $h (- 3 i)$ and $3 h i$ .

$h - 3 i h + h + 3 i h$

Add $- 3 i h$ and $3 i h$ .

$h + h + 0$

Add $h + h$ and $0$ .

$h + h$

Add $h$ and $h$ .

$2 h$

Simplify (h^2i-3h^2i^2)/(hi)+(3h^2+9h^2i)/(3h)

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