Simplify 5/(12x^2y)-11/(6xy)

$\frac{5}{12 x^{2} y} - \frac{11}{6 x y}$

Step 1

To write $- \frac{11}{6 x y}$ as a fraction with a common denominator, multiply by $\frac{2 x}{2 x}$ .

$\frac{5}{12 x^{2} y} - \frac{11}{6 x y} \cdot \frac{2 x}{2 x}$

Step 2

Write each expression with a common denominator of $12 y x^{2}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{11}{6 x y}$ by $\frac{2 x}{2 x}$ .

$\frac{5}{12 x^{2} y} - \frac{11 (2 x)}{6 x y (2 x)}$

Multiply $2$ by $6$ .

$\frac{5}{12 x^{2} y} - \frac{11 (2 x)}{12 x y x}$

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

$\frac{5}{12 x^{2} y} - \frac{11 (2 x)}{12 (x^{1} x) y}$

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

$\frac{5}{12 x^{2} y} - \frac{11 (2 x)}{12 (x^{1} x^{1}) y}$

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

$\frac{5}{12 x^{2} y} - \frac{11 (2 x)}{12 x^{1 + 1} y}$

Add $1$ and $1$ .

$\frac{5}{12 x^{2} y} - \frac{11 (2 x)}{12 x^{2} y}$

Step 3

Combine the numerators over the common denominator.

$\frac{5 - 11 (2 x)}{12 x^{2} y}$

Step 4

Multiply $- 11$ by $2$ .

$\frac{5 - 22 x}{12 x^{2} y}$