Pre-Algebra Examples

$\frac{1}{b} + \frac{1}{b - 4} = \frac{b - 3}{b - 4}$

Step 1

Simplify $\frac{1}{b} + \frac{1}{b - 4}$ .

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Step 1.1

To write $\frac{1}{b}$ as a fraction with a common denominator, multiply by $\frac{b - 4}{b - 4}$ .

$\frac{1}{b} \cdot \frac{b - 4}{b - 4} + \frac{1}{b - 4} = \frac{b - 3}{b - 4}$

Step 1.2

To write $\frac{1}{b - 4}$ as a fraction with a common denominator, multiply by $\frac{b}{b}$ .

$\frac{1}{b} \cdot \frac{b - 4}{b - 4} + \frac{1}{b - 4} \cdot \frac{b}{b} = \frac{b - 3}{b - 4}$

Step 1.3

Write each expression with a common denominator of $b (b - 4)$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{1}{b}$ by $\frac{b - 4}{b - 4}$ .

$\frac{b - 4}{b (b - 4)} + \frac{1}{b - 4} \cdot \frac{b}{b} = \frac{b - 3}{b - 4}$

Step 1.3.2

Multiply $\frac{1}{b - 4}$ by $\frac{b}{b}$ .

$\frac{b - 4}{b (b - 4)} + \frac{b}{(b - 4) b} = \frac{b - 3}{b - 4}$

Step 1.3.3

Reorder the factors of $(b - 4) b$ .

$\frac{b - 4}{b (b - 4)} + \frac{b}{b (b - 4)} = \frac{b - 3}{b - 4}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{b - 4 + b}{b (b - 4)} = \frac{b - 3}{b - 4}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Add $b$ and $b$ .

$\frac{2 b - 4}{b (b - 4)} = \frac{b - 3}{b - 4}$

Step 1.5.2

Factor $2$ out of $2 b - 4$ .

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Step 1.5.2.1

Factor $2$ out of $2 b$ .

$\frac{2 (b) - 4}{b (b - 4)} = \frac{b - 3}{b - 4}$

Step 1.5.2.2

Factor $2$ out of $- 4$ .

$\frac{2 b + 2 \cdot - 2}{b (b - 4)} = \frac{b - 3}{b - 4}$

Step 1.5.2.3

Factor $2$ out of $2 b + 2 \cdot - 2$ .

$\frac{2 (b - 2)}{b (b - 4)} = \frac{b - 3}{b - 4}$

Step 2

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

$b = 1$

Step 3