Simplify 5/(4x^2y)-y/(14xz)

$\frac{5}{4 x^{2} y} - \frac{y}{14 x z}$

Step 1

To write $\frac{5}{4 x^{2} y}$ as a fraction with a common denominator, multiply by $\frac{7 z}{7 z}$ .

$\frac{5}{4 x^{2} y} \cdot \frac{7 z}{7 z} - \frac{y}{14 x z}$

Step 2

To write $- \frac{y}{14 x z}$ as a fraction with a common denominator, multiply by $\frac{2 y x}{2 y x}$ .

$\frac{5}{4 x^{2} y} \cdot \frac{7 z}{7 z} - \frac{y}{14 x z} \cdot \frac{2 y x}{2 y x}$

Step 3

Write each expression with a common denominator of $28 y z x^{2}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{4 x^{2} y}$ by $\frac{7 z}{7 z}$ .

$\frac{5 (7 z)}{4 x^{2} y (7 z)} - \frac{y}{14 x z} \cdot \frac{2 y x}{2 y x}$

Multiply $7$ by $4$ .

$\frac{5 (7 z)}{28 x^{2} y z} - \frac{y}{14 x z} \cdot \frac{2 y x}{2 y x}$

Multiply $\frac{y}{14 x z}$ by $\frac{2 y x}{2 y x}$ .

$\frac{5 (7 z)}{28 x^{2} y z} - \frac{y (2 y x)}{14 x z (2 y x)}$

Multiply $2$ by $14$ .

$\frac{5 (7 z)}{28 x^{2} y z} - \frac{y (2 y x)}{28 x z (y x)}$

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

$\frac{5 (7 z)}{28 x^{2} y z} - \frac{y (2 y x)}{28 (x^{1} x) z y}$

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

$\frac{5 (7 z)}{28 x^{2} y z} - \frac{y (2 y x)}{28 (x^{1} x^{1}) z y}$

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

$\frac{5 (7 z)}{28 x^{2} y z} - \frac{y (2 y x)}{28 x^{1 + 1} z y}$

Add $1$ and $1$ .

$\frac{5 (7 z)}{28 x^{2} y z} - \frac{y (2 y x)}{28 x^{2} z y}$

Reorder the factors of $28 x^{2} z y$ .

$\frac{5 (7 z)}{28 x^{2} y z} - \frac{y (2 y x)}{28 x^{2} y z}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 (7 z) - y (2 y x)}{28 x^{2} y z}$

Step 5

Simplify the numerator.

Multiply $5$ by $7$ .

$\frac{35 z - y (2 y x)}{28 x^{2} y z}$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$\frac{35 z - (y \cdot y) (2 x)}{28 x^{2} y z}$

Multiply $y$ by $y$ .

$\frac{35 z - y^{2} (2 x)}{28 x^{2} y z}$

Rewrite using the commutative property of multiplication.

$\frac{35 z - 1 \cdot 2 y^{2} x}{28 x^{2} y z}$

Multiply $- 1$ by $2$ .

$\frac{35 z - 2 y^{2} x}{28 x^{2} y z}$