Simplify 7/(25z^3y)-1/(35z^2y)

$\frac{7}{25 z^{3} y} - \frac{1}{35 z^{2} y}$

To write $\frac{7}{25 z^{3} y}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{7}{25 z^{3} y} \cdot \frac{7}{7} - \frac{1}{35 z^{2} y}$

To write $- \frac{1}{35 z^{2} y}$ as a fraction with a common denominator, multiply by $\frac{5 z}{5 z}$ .

$\frac{7}{25 z^{3} y} \cdot \frac{7}{7} - \frac{1}{35 z^{2} y} \cdot \frac{5 z}{5 z}$

Write each expression with a common denominator of $175 y z^{3}$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{7}{25 z^{3} y}$ and $\frac{7}{7}$ .

$\frac{7 \cdot 7}{25 z^{3} y \cdot 7} - \frac{1}{35 z^{2} y} \cdot \frac{5 z}{5 z}$

Multiply $7$ by $25$ .

$\frac{7 \cdot 7}{175 z^{3} y} - \frac{1}{35 z^{2} y} \cdot \frac{5 z}{5 z}$

Multiply $\frac{1}{35 z^{2} y}$ and $\frac{5 z}{5 z}$ .

$\frac{7 \cdot 7}{175 z^{3} y} - \frac{5 z}{35 z^{2} y (5 z)}$

Multiply $5$ by $35$ .

$\frac{7 \cdot 7}{175 z^{3} y} - \frac{5 z}{175 z^{2} y z}$

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

$\frac{7 \cdot 7}{175 z^{3} y} - \frac{5 z}{175 y (z^{2} z^{1})}$

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

$\frac{7 \cdot 7}{175 z^{3} y} - \frac{5 z}{175 y z^{2 + 1}}$

Add $2$ and $1$ .

$\frac{7 \cdot 7}{175 z^{3} y} - \frac{5 z}{175 y z^{3}}$

Reorder the factors of $175 y z^{3}$ .

$\frac{7 \cdot 7}{175 z^{3} y} - \frac{5 z}{175 z^{3} y}$

Combine the numerators over the common denominator.

$\frac{7 \cdot 7 - 5 z}{175 z^{3} y}$

Multiply $7$ by $7$ .

$\frac{49 - 5 z}{175 z^{3} y}$

Simplify 7/(25z^3y)-1/(35z^2y)

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