Pre-Algebra Examples

$\frac{3 b}{b - 8} - 8 = \frac{1}{b - 8}$

Step 1

Simplify $\frac{3 b}{b - 8} - 8$ .

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Step 1.1

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

$\frac{3 b}{b - 8} - 8 \cdot \frac{b - 8}{b - 8} = \frac{1}{b - 8}$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine $- 8$ and $\frac{b - 8}{b - 8}$ .

$\frac{3 b}{b - 8} + \frac{- 8 (b - 8)}{b - 8} = \frac{1}{b - 8}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{3 b - 8 (b - 8)}{b - 8} = \frac{1}{b - 8}$

Step 1.3

Simplify the numerator.

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Step 1.3.1

Apply the distributive property.

$\frac{3 b - 8 b - 8 \cdot - 8}{b - 8} = \frac{1}{b - 8}$

Step 1.3.2

Multiply $- 8$ by $- 8$ .

$\frac{3 b - 8 b + 64}{b - 8} = \frac{1}{b - 8}$

Step 1.3.3

Subtract $8 b$ from $3 b$ .

$\frac{- 5 b + 64}{b - 8} = \frac{1}{b - 8}$

Step 1.4

Simplify with factoring out.

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Step 1.4.1

Factor $- 1$ out of $- 5 b$ .

$\frac{- (5 b) + 64}{b - 8} = \frac{1}{b - 8}$

Step 1.4.2

Rewrite $64$ as $- 1 (- 64)$ .

$\frac{- (5 b) - 1 (- 64)}{b - 8} = \frac{1}{b - 8}$

Step 1.4.3

Factor $- 1$ out of $- (5 b) - 1 (- 64)$ .

$\frac{- (5 b - 64)}{b - 8} = \frac{1}{b - 8}$

Step 1.4.4

Simplify the expression.

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Step 1.4.4.1

Rewrite $- (5 b - 64)$ as $- 1 (5 b - 64)$ .

$\frac{- 1 (5 b - 64)}{b - 8} = \frac{1}{b - 8}$

Step 1.4.4.2

Move the negative in front of the fraction.

$- \frac{5 b - 64}{b - 8} = \frac{1}{b - 8}$

Step 2

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

$b \approx 12.6$

Step 3