Basic Math Examples

$\frac{5}{3 (y - 1)} - \frac{4}{2 (y - 1)}$

Step 1

Cancel the common factor of $4$ and $2$ .

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Step 1.1

Factor $2$ out of $4$ .

$\frac{5}{3 (y - 1)} - \frac{2 \cdot 2}{2 (y - 1)}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Cancel the common factor.

$\frac{5}{3 (y - 1)} - \frac{2 \cdot 2}{2 (y - 1)}$

Step 1.2.2

Rewrite the expression.

$\frac{5}{3 (y - 1)} - \frac{2}{y - 1}$

Step 2

To write $- \frac{2}{y - 1}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5}{3 (y - 1)} - \frac{2}{y - 1} \cdot \frac{3}{3}$

Step 3

Write each expression with a common denominator of $3 (y - 1)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{2}{y - 1}$ by $\frac{3}{3}$ .

$\frac{5}{3 (y - 1)} - \frac{2 \cdot 3}{(y - 1) \cdot 3}$

Step 3.2

Reorder the factors of $(y - 1) \cdot 3$ .

$\frac{5}{3 (y - 1)} - \frac{2 \cdot 3}{3 (y - 1)}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 - 2 \cdot 3}{3 (y - 1)}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 2$ by $3$ .

$\frac{5 - 6}{3 (y - 1)}$

Step 5.2

Subtract $6$ from $5$ .

$\frac{- 1}{3 (y - 1)}$

Step 6

Move the negative in front of the fraction.

$- \frac{1}{3 (y - 1)}$