Basic Math Examples

$\frac{5}{4 b} - \frac{6}{b - 1}$

Step 1

To write $\frac{5}{4 b}$ as a fraction with a common denominator, multiply by $\frac{b - 1}{b - 1}$ .

$\frac{5}{4 b} \cdot \frac{b - 1}{b - 1} - \frac{6}{b - 1}$

Step 2

To write $- \frac{6}{b - 1}$ as a fraction with a common denominator, multiply by $\frac{4 b}{4 b}$ .

$\frac{5}{4 b} \cdot \frac{b - 1}{b - 1} - \frac{6}{b - 1} \cdot \frac{4 b}{4 b}$

Step 3

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

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Step 3.1

Multiply $\frac{5}{4 b}$ by $\frac{b - 1}{b - 1}$ .

$\frac{5 (b - 1)}{4 b (b - 1)} - \frac{6}{b - 1} \cdot \frac{4 b}{4 b}$

Step 3.2

Multiply $\frac{6}{b - 1}$ by $\frac{4 b}{4 b}$ .

$\frac{5 (b - 1)}{4 b (b - 1)} - \frac{6 (4 b)}{(b - 1) (4 b)}$

Step 3.3

Reorder the factors of $(b - 1) (4 b)$ .

$\frac{5 (b - 1)}{4 b (b - 1)} - \frac{6 (4 b)}{4 b (b - 1)}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 (b - 1) - 6 (4 b)}{4 b (b - 1)}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{5 b + 5 \cdot - 1 - 6 \cdot 4 b}{4 b (b - 1)}$

Step 5.2

Multiply $5$ by $- 1$ .

$\frac{5 b - 5 - 6 \cdot 4 b}{4 b (b - 1)}$

Step 5.3

Multiply $- 6$ by $4$ .

$\frac{5 b - 5 - 24 b}{4 b (b - 1)}$

Step 5.4

Subtract $24 b$ from $5 b$ .

$\frac{- 19 b - 5}{4 b (b - 1)}$

Step 6

Simplify with factoring out.

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Step 6.1

Factor $- 1$ out of $- 19 b$ .

$\frac{- (19 b) - 5}{4 b (b - 1)}$

Step 6.2

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

$\frac{- (19 b) - 1 (5)}{4 b (b - 1)}$

Step 6.3

Factor $- 1$ out of $- (19 b) - 1 (5)$ .

$\frac{- (19 b + 5)}{4 b (b - 1)}$

Step 6.4

Simplify the expression.

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Step 6.4.1

Rewrite $- (19 b + 5)$ as $- 1 (19 b + 5)$ .

$\frac{- 1 (19 b + 5)}{4 b (b - 1)}$

Step 6.4.2

Move the negative in front of the fraction.

$- \frac{19 b + 5}{4 b (b - 1)}$