Basic Math Examples

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

Step 1

Reduce the expression $\frac{(2 m + 3) (m - 4)}{(m - 4) (m - 6)}$ by cancelling the common factors.

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Step 1.1

Cancel the common factor.

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

Step 1.2

Rewrite the expression.

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

Step 2

Rewrite the division as a fraction.

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

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{2 m + 3}{m - 6} \cdot \frac{1}{m - 6} \cdot \frac{m - 3}{(2 m - 3) (2 m + 3)}$

Step 4

Multiply $\frac{2 m + 3}{m - 6} \cdot \frac{1}{m - 6}$ .

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Step 4.1

Multiply $\frac{2 m + 3}{m - 6}$ by $\frac{1}{m - 6}$ .

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

Step 4.2

Raise $m - 6$ to the power of $1$ .

$\frac{2 m + 3}{{(m - 6)}^{1} (m - 6)} \cdot \frac{m - 3}{(2 m - 3) (2 m + 3)}$

Step 4.3

Raise $m - 6$ to the power of $1$ .

$\frac{2 m + 3}{{(m - 6)}^{1} {(m - 6)}^{1}} \cdot \frac{m - 3}{(2 m - 3) (2 m + 3)}$

Step 4.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2 m + 3}{{(m - 6)}^{1 + 1}} \cdot \frac{m - 3}{(2 m - 3) (2 m + 3)}$

Step 4.5

Add $1$ and $1$ .

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

Step 5

Cancel the common factor of $2 m + 3$ .

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Step 5.1

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

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

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

$\frac{1}{{(m - 6)}^{2}} \cdot \frac{m - 3}{2 m - 3}$

Step 6

Multiply $\frac{1}{{(m - 6)}^{2}}$ by $\frac{m - 3}{2 m - 3}$ .

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