Simplify 19/(xy^2)-(7y^2)/(8x^2)

$\frac{19}{x y^{2}} - \frac{7 y^{2}}{8 x^{2}}$

Step 1

To write $\frac{19}{x y^{2}}$ as a fraction with a common denominator, multiply by $\frac{8 x}{8 x}$ .

$\frac{19}{x y^{2}} \cdot \frac{8 x}{8 x} - \frac{7 y^{2}}{8 x^{2}}$

Step 2

To write $- \frac{7 y^{2}}{8 x^{2}}$ as a fraction with a common denominator, multiply by $\frac{y^{2}}{y^{2}}$ .

$\frac{19}{x y^{2}} \cdot \frac{8 x}{8 x} - \frac{7 y^{2}}{8 x^{2}} \cdot \frac{y^{2}}{y^{2}}$

Step 3

Write each expression with a common denominator of $8 x^{2} y^{2}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{19}{x y^{2}}$ by $\frac{8 x}{8 x}$ .

$\frac{19 (8 x)}{x y^{2} (8 x)} - \frac{7 y^{2}}{8 x^{2}} \cdot \frac{y^{2}}{y^{2}}$

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

$\frac{19 (8 x)}{x^{1} x y^{2} \cdot 8} - \frac{7 y^{2}}{8 x^{2}} \cdot \frac{y^{2}}{y^{2}}$

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

$\frac{19 (8 x)}{x^{1} x^{1} y^{2} \cdot 8} - \frac{7 y^{2}}{8 x^{2}} \cdot \frac{y^{2}}{y^{2}}$

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

$\frac{19 (8 x)}{x^{1 + 1} y^{2} \cdot 8} - \frac{7 y^{2}}{8 x^{2}} \cdot \frac{y^{2}}{y^{2}}$

Add $1$ and $1$ .

$\frac{19 (8 x)}{x^{2} y^{2} \cdot 8} - \frac{7 y^{2}}{8 x^{2}} \cdot \frac{y^{2}}{y^{2}}$

Multiply $\frac{7 y^{2}}{8 x^{2}}$ by $\frac{y^{2}}{y^{2}}$ .

$\frac{19 (8 x)}{x^{2} y^{2} \cdot 8} - \frac{7 y^{2} y^{2}}{8 x^{2} y^{2}}$

Reorder the factors of $x^{2} y^{2} \cdot 8$ .

$\frac{19 (8 x)}{8 x^{2} y^{2}} - \frac{7 y^{2} y^{2}}{8 x^{2} y^{2}}$

Step 4

Combine the numerators over the common denominator.

$\frac{19 (8 x) - 7 y^{2} y^{2}}{8 x^{2} y^{2}}$

Step 5

Simplify the numerator.

Multiply $19$ by $8$ .

$\frac{152 x - 7 y^{2} y^{2}}{8 x^{2} y^{2}}$

Multiply $y^{2}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$\frac{152 x - 7 (y^{2} y^{2})}{8 x^{2} y^{2}}$

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

$\frac{152 x - 7 y^{2 + 2}}{8 x^{2} y^{2}}$

Add $2$ and $2$ .

$\frac{152 x - 7 y^{4}}{8 x^{2} y^{2}}$