Pre-Algebra Examples

$\frac{x - 7}{8 y} - \frac{y}{5 x}$

Step 1

To write $\frac{x - 7}{8 y}$ as a fraction with a common denominator, multiply by $\frac{5 x}{5 x}$ .

$\frac{x - 7}{8 y} \cdot \frac{5 x}{5 x} - \frac{y}{5 x}$

Step 2

To write $- \frac{y}{5 x}$ as a fraction with a common denominator, multiply by $\frac{8 y}{8 y}$ .

$\frac{x - 7}{8 y} \cdot \frac{5 x}{5 x} - \frac{y}{5 x} \cdot \frac{8 y}{8 y}$

Step 3

Write each expression with a common denominator of $40 y x$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{x - 7}{8 y}$ by $\frac{5 x}{5 x}$ .

$\frac{(x - 7) (5 x)}{8 y (5 x)} - \frac{y}{5 x} \cdot \frac{8 y}{8 y}$

Step 3.2

Multiply $5$ by $8$ .

$\frac{(x - 7) (5 x)}{40 y x} - \frac{y}{5 x} \cdot \frac{8 y}{8 y}$

Step 3.3

Multiply $\frac{y}{5 x}$ by $\frac{8 y}{8 y}$ .

$\frac{(x - 7) (5 x)}{40 y x} - \frac{y (8 y)}{5 x (8 y)}$

Step 3.4

Multiply $8$ by $5$ .

$\frac{(x - 7) (5 x)}{40 y x} - \frac{y (8 y)}{40 x y}$

Step 3.5

Reorder the factors of $40 y x$ .

$\frac{(x - 7) (5 x)}{40 x y} - \frac{y (8 y)}{40 x y}$

Step 4

Combine the numerators over the common denominator.

$\frac{(x - 7) (5 x) - y (8 y)}{40 x y}$

Step 5

Rewrite $\frac{(x - 7) (5 x) - y (8 y)}{40 x y}$ in a factored form.

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Step 5.1

Apply the distributive property.

$\frac{x (5 x) - 7 (5 x) - y (8 y)}{40 x y}$

Step 5.2

Rewrite using the commutative property of multiplication.

$\frac{5 x \cdot x - 7 (5 x) - y (8 y)}{40 x y}$

Step 5.3

Multiply $5$ by $- 7$ .

$\frac{5 x \cdot x - 35 x - y (8 y)}{40 x y}$

Step 5.4

Multiply $x$ by $x$ by adding the exponents.

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Step 5.4.1

Move $x$ .

$\frac{5 (x \cdot x) - 35 x - y (8 y)}{40 x y}$

Step 5.4.2

Multiply $x$ by $x$ .

$\frac{5 x^{2} - 35 x - y (8 y)}{40 x y}$

Step 5.5

Rewrite using the commutative property of multiplication.

$\frac{5 x^{2} - 35 x - 1 \cdot 8 y \cdot y}{40 x y}$

Step 5.6

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

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Step 5.6.1

Move $y$ .

$\frac{5 x^{2} - 35 x - 1 \cdot 8 (y \cdot y)}{40 x y}$

Step 5.6.2

Multiply $y$ by $y$ .

$\frac{5 x^{2} - 35 x - 1 \cdot 8 y^{2}}{40 x y}$

Step 5.7

Multiply $- 1$ by $8$ .

$\frac{5 x^{2} - 35 x - 8 y^{2}}{40 x y}$