Simplify (6x^2)/(2xy)+(8z)/(xz)

$\frac{6 x^{2}}{2 x y} + \frac{8 z}{x z}$

Step 1

Simplify each term.

Cancel the common factor of $6$ and $2$ .

Factor $2$ out of $6 x^{2}$ .

$\frac{2 (3 x^{2})}{2 x y} + \frac{8 z}{x z}$

Cancel the common factors.

Factor $2$ out of $2 x y$ .

$\frac{2 (3 x^{2})}{2 (x y)} + \frac{8 z}{x z}$

Cancel the common factor.

$\frac{2 (3 x^{2})}{2 (x y)} + \frac{8 z}{x z}$

Rewrite the expression.

$\frac{3 x^{2}}{x y} + \frac{8 z}{x z}$

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

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

$\frac{x (3 x)}{x y} + \frac{8 z}{x z}$

Cancel the common factors.

Factor $x$ out of $x y$ .

$\frac{x (3 x)}{x (y)} + \frac{8 z}{x z}$

Cancel the common factor.

$\frac{x (3 x)}{x y} + \frac{8 z}{x z}$

Rewrite the expression.

$\frac{3 x}{y} + \frac{8 z}{x z}$

Cancel the common factor of $z$ .

Cancel the common factor.

$\frac{3 x}{y} + \frac{8 z}{x z}$

Rewrite the expression.

$\frac{3 x}{y} + \frac{8}{x}$

Step 2

To write $\frac{3 x}{y}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{3 x}{y} \cdot \frac{x}{x} + \frac{8}{x}$

Step 3

To write $\frac{8}{x}$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$\frac{3 x}{y} \cdot \frac{x}{x} + \frac{8}{x} \cdot \frac{y}{y}$

Step 4

Write each expression with a common denominator of $y x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3 x}{y}$ by $\frac{x}{x}$ .

$\frac{3 x \cdot x}{y x} + \frac{8}{x} \cdot \frac{y}{y}$

Multiply $\frac{8}{x}$ by $\frac{y}{y}$ .

$\frac{3 x \cdot x}{y x} + \frac{8 y}{x y}$

Reorder the factors of $y x$ .

$\frac{3 x \cdot x}{x y} + \frac{8 y}{x y}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 x \cdot x + 8 y}{x y}$

Step 6

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$\frac{3 (x \cdot x) + 8 y}{x y}$

Multiply $x$ by $x$ .

$\frac{3 x^{2} + 8 y}{x y}$

Simplify (6x^2)/(2xy)+(8z)/(xz)

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