Simplify 8/(5x^4y^2z)-4/(10xy^3)

$\frac{8}{5 x^{4} y^{2} z} - \frac{4}{10 x y^{3}}$

Cancel the common factor of $4$ and $10$ .

Factor $2$ out of $4$ .

$\frac{8}{5 x^{4} y^{2} z} - \frac{2 (2)}{10 x y^{3}}$

Cancel the common factors.

Factor $2$ out of $10 x y^{3}$ .

$\frac{8}{5 x^{4} y^{2} z} - \frac{2 (2)}{2 (5 x y^{3})}$

Cancel the common factor.

$\frac{8}{5 x^{4} y^{2} z} - \frac{2 \cdot 2}{2 (5 x y^{3})}$

Rewrite the expression.

$\frac{8}{5 x^{4} y^{2} z} - \frac{2}{5 x y^{3}}$

To write $\frac{8}{5 x^{4} y^{2} z}$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$\frac{8}{5 x^{4} y^{2} z} \cdot \frac{y}{y} - \frac{2}{5 x y^{3}}$

To write $- \frac{2}{5 x y^{3}}$ as a fraction with a common denominator, multiply by $\frac{z x^{3}}{z x^{3}}$ .

$\frac{8}{5 x^{4} y^{2} z} \cdot \frac{y}{y} - \frac{2}{5 x y^{3}} \cdot \frac{z x^{3}}{z x^{3}}$

Write each expression with a common denominator of $5 z x^{4} y^{3}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{8}{5 x^{4} y^{2} z}$ by $\frac{y}{y}$ .

$\frac{8 y}{5 x^{4} y^{2} z y} - \frac{2}{5 x y^{3}} \cdot \frac{z x^{3}}{z x^{3}}$

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

$\frac{8 y}{5 x^{4} (y^{1} y^{2}) z} - \frac{2}{5 x y^{3}} \cdot \frac{z x^{3}}{z x^{3}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{8 y}{5 x^{4} y^{1 + 2} z} - \frac{2}{5 x y^{3}} \cdot \frac{z x^{3}}{z x^{3}}$

Add $1$ and $2$ .

$\frac{8 y}{5 x^{4} y^{3} z} - \frac{2}{5 x y^{3}} \cdot \frac{z x^{3}}{z x^{3}}$

Multiply $\frac{2}{5 x y^{3}}$ by $\frac{z x^{3}}{z x^{3}}$ .

$\frac{8 y}{5 x^{4} y^{3} z} - \frac{2 (z x^{3})}{5 x y^{3} (z x^{3})}$

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

$\frac{8 y}{5 x^{4} y^{3} z} - \frac{2 (z x^{3})}{5 (x^{3} x^{1}) y^{3} z}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{8 y}{5 x^{4} y^{3} z} - \frac{2 (z x^{3})}{5 x^{3 + 1} y^{3} z}$

Add $3$ and $1$ .

$\frac{8 y}{5 x^{4} y^{3} z} - \frac{2 (z x^{3})}{5 x^{4} y^{3} z}$

Combine the numerators over the common denominator.

$\frac{8 y - 2 (z x^{3})}{5 x^{4} y^{3} z}$

Factor $2$ out of $8 y - 2 z x^{3}$ .

Factor $2$ out of $8 y$ .

$\frac{2 (4 y) - 2 z x^{3}}{5 x^{4} y^{3} z}$

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

$\frac{2 (4 y) + 2 (- z x^{3})}{5 x^{4} y^{3} z}$

Factor $2$ out of $2 (4 y) + 2 (- z x^{3})$ .

$\frac{2 (4 y - z x^{3})}{5 x^{4} y^{3} z}$