Basic Math Examples

$\frac{3}{2 m} + \frac{2 m}{6 m - 4}$

Step 1

Cancel the common factor of $2$ and $6 m - 4$ .

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Step 1.1

Factor $2$ out of $2 m$ .

$\frac{3}{2 m} + \frac{2 (m)}{6 m - 4}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $6 m$ .

$\frac{3}{2 m} + \frac{2 (m)}{2 (3 m) - 4}$

Step 1.2.2

Factor $2$ out of $- 4$ .

$\frac{3}{2 m} + \frac{2 (m)}{2 (3 m) + 2 (- 2)}$

Step 1.2.3

Factor $2$ out of $2 (3 m) + 2 (- 2)$ .

$\frac{3}{2 m} + \frac{2 (m)}{2 (3 m - 2)}$

Step 1.2.4

Cancel the common factor.

$\frac{3}{2 m} + \frac{2 m}{2 (3 m - 2)}$

Step 1.2.5

Rewrite the expression.

$\frac{3}{2 m} + \frac{m}{3 m - 2}$

Step 2

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

$\frac{3}{2 m} \cdot \frac{3 m - 2}{3 m - 2} + \frac{m}{3 m - 2}$

Step 3

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

$\frac{3}{2 m} \cdot \frac{3 m - 2}{3 m - 2} + \frac{m}{3 m - 2} \cdot \frac{2 m}{2 m}$

Step 4

Write each expression with a common denominator of $2 m (3 m - 2)$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{3}{2 m}$ by $\frac{3 m - 2}{3 m - 2}$ .

$\frac{3 (3 m - 2)}{2 m (3 m - 2)} + \frac{m}{3 m - 2} \cdot \frac{2 m}{2 m}$

Step 4.2

Multiply $\frac{m}{3 m - 2}$ by $\frac{2 m}{2 m}$ .

$\frac{3 (3 m - 2)}{2 m (3 m - 2)} + \frac{m (2 m)}{(3 m - 2) (2 m)}$

Step 4.3

Reorder the factors of $(3 m - 2) (2 m)$ .

$\frac{3 (3 m - 2)}{2 m (3 m - 2)} + \frac{m (2 m)}{2 m (3 m - 2)}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 (3 m - 2) + m (2 m)}{2 m (3 m - 2)}$

Step 6

Simplify the numerator.

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Step 6.1

Apply the distributive property.

$\frac{3 (3 m) + 3 \cdot - 2 + m (2 m)}{2 m (3 m - 2)}$

Step 6.2

Multiply $3$ by $3$ .

$\frac{9 m + 3 \cdot - 2 + m (2 m)}{2 m (3 m - 2)}$

Step 6.3

Multiply $3$ by $- 2$ .

$\frac{9 m - 6 + m (2 m)}{2 m (3 m - 2)}$

Step 6.4

Rewrite using the commutative property of multiplication.

$\frac{9 m - 6 + 2 m \cdot m}{2 m (3 m - 2)}$

Step 6.5

Multiply $m$ by $m$ by adding the exponents.

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Step 6.5.1

Move $m$ .

$\frac{9 m - 6 + 2 (m \cdot m)}{2 m (3 m - 2)}$

Step 6.5.2

Multiply $m$ by $m$ .

$\frac{9 m - 6 + 2 m^{2}}{2 m (3 m - 2)}$

Step 6.6

Reorder terms.

$\frac{2 m^{2} + 9 m - 6}{2 m (3 m - 2)}$