Simplify 3/(7z)-6/(49yz^4)

$\frac{3}{7 z} - \frac{6}{49 y z^{4}}$

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

$\frac{3}{7 z} \cdot \frac{7 y z^{3}}{7 y z^{3}} - \frac{6}{49 y z^{4}}$

Write each expression with a common denominator of $49 y z^{4}$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{3 (7 y z^{3})}{7 z (7 y z^{3})} - \frac{6}{49 y z^{4}}$

Multiply $7$ by $7$ .

$\frac{3 (7 y z^{3})}{49 z (y z^{3})} - \frac{6}{49 y z^{4}}$

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

$\frac{3 (7 y z^{3})}{49 (y (z^{1} z^{3}))} - \frac{6}{49 y z^{4}}$

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

$\frac{3 (7 y z^{3})}{49 (y z^{1 + 3})} - \frac{6}{49 y z^{4}}$

Add $1$ and $3$ .

$\frac{3 (7 y z^{3})}{49 (y z^{4})} - \frac{6}{49 y z^{4}}$

Reorder the factors of $49 (y z^{4})$ .

$\frac{3 (7 y z^{3})}{49 z^{4} y} - \frac{6}{49 y z^{4}}$

Reorder the factors of $49 y z^{4}$ .

$\frac{3 (7 y z^{3})}{49 z^{4} y} - \frac{6}{49 z^{4} y}$

Combine the numerators over the common denominator.

$\frac{3 (7 y z^{3}) - 6}{49 z^{4} y}$

Factor $3$ out of $3 \cdot 7 y z^{3} - 6$ .

Factor $3$ out of $- 6$ .

$\frac{3 (7 y z^{3}) + 3 \cdot - 2}{49 z^{4} y}$

Factor $3$ out of $3 (7 y z^{3}) + 3 \cdot - 2$ .

$\frac{3 (7 y z^{3} - 2)}{49 z^{4} y}$