Pre-Algebra Examples

$\frac{10}{x} - \frac{10}{x - 8} = - 4$

Step 1

Simplify $\frac{10}{x} - \frac{10}{x - 8}$ .

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Step 1.1

To write $\frac{10}{x}$ as a fraction with a common denominator, multiply by $\frac{x - 8}{x - 8}$ .

$\frac{10}{x} \cdot \frac{x - 8}{x - 8} - \frac{10}{x - 8} = - 4$

Step 1.2

To write $- \frac{10}{x - 8}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{10}{x} \cdot \frac{x - 8}{x - 8} - \frac{10}{x - 8} \cdot \frac{x}{x} = - 4$

Step 1.3

Write each expression with a common denominator of $x (x - 8)$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{10}{x}$ by $\frac{x - 8}{x - 8}$ .

$\frac{10 (x - 8)}{x (x - 8)} - \frac{10}{x - 8} \cdot \frac{x}{x} = - 4$

Step 1.3.2

Multiply $\frac{10}{x - 8}$ by $\frac{x}{x}$ .

$\frac{10 (x - 8)}{x (x - 8)} - \frac{10 x}{(x - 8) x} = - 4$

Step 1.3.3

Reorder the factors of $(x - 8) x$ .

$\frac{10 (x - 8)}{x (x - 8)} - \frac{10 x}{x (x - 8)} = - 4$

Step 1.4

Combine the numerators over the common denominator.

$\frac{10 (x - 8) - 10 x}{x (x - 8)} = - 4$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Factor $10$ out of $10 (x - 8) - 10 x$ .

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Step 1.5.1.1

Factor $10$ out of $- 10 x$ .

$\frac{10 (x - 8) + 10 (- x)}{x (x - 8)} = - 4$

Step 1.5.1.2

Factor $10$ out of $10 (x - 8) + 10 (- x)$ .

$\frac{10 (x - 8 - x)}{x (x - 8)} = - 4$

Step 1.5.2

Subtract $x$ from $x$ .

$\frac{10 (0 - 8)}{x (x - 8)} = - 4$

Step 1.5.3

Subtract $8$ from $0$ .

$\frac{10 \cdot - 8}{x (x - 8)} = - 4$

Step 1.6

Simplify the expression.

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Step 1.6.1

Multiply $10$ by $- 8$ .

$\frac{- 80}{x (x - 8)} = - 4$

Step 1.6.2

Move the negative in front of the fraction.

$- \frac{80}{x (x - 8)} = - 4$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = - 2, 10$

Step 3