Basic Math Examples

\frac{a^{2} + (2 a - 3) (a + 2)}{a (a - 2)} \cdot \frac{a - 2}{2 a - 3}

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

Step 1

Simplify the numerator.

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Step 1.1

Expand

(2 a - 3) (a + 2)

$(2 a - 3) (a + 2)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

\frac{a^{2} + 2 a (a + 2) - 3 (a + 2)}{a (a - 2)} \cdot \frac{a - 2}{2 a - 3}

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

Step 1.1.2

Apply the distributive property.

\frac{a^{2} + 2 a \cdot a + 2 a \cdot 2 - 3 (a + 2)}{a (a - 2)} \cdot \frac{a - 2}{2 a - 3}

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

Step 1.1.3

Apply the distributive property.

\frac{a^{2} + 2 a \cdot a + 2 a \cdot 2 - 3 a - 3 \cdot 2}{a (a - 2)} \cdot \frac{a - 2}{2 a - 3}

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

\frac{a^{2} + 2 a \cdot a + 2 a \cdot 2 - 3 a - 3 \cdot 2}{a (a - 2)} \cdot \frac{a - 2}{2 a - 3}

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

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Multiply

a

$a$ by

a

$a$ by adding the exponents.

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Step 1.2.1.1.1

Move

a

$a$ .

\frac{a^{2} + 2 (a \cdot a) + 2 a \cdot 2 - 3 a - 3 \cdot 2}{a (a - 2)} \cdot \frac{a - 2}{2 a - 3}

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

Step 1.2.1.1.2

Multiply

a

$a$ by

a

$a$ .

\frac{a^{2} + 2 a^{2} + 2 a \cdot 2 - 3 a - 3 \cdot 2}{a (a - 2)} \cdot \frac{a - 2}{2 a - 3}

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

\frac{a^{2} + 2 a^{2} + 2 a \cdot 2 - 3 a - 3 \cdot 2}{a (a - 2)} \cdot \frac{a - 2}{2 a - 3}

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

Step 1.2.1.2

Multiply

2

$2$ by

2

$2$ .

\frac{a^{2} + 2 a^{2} + 4 a - 3 a - 3 \cdot 2}{a (a - 2)} \cdot \frac{a - 2}{2 a - 3}

$\frac{a^{2} + 2 a^{2} + 4 a - 3 a - 3 \cdot 2}{a (a - 2)} \cdot \frac{a - 2}{2 a - 3}$

Step 1.2.1.3

Multiply

- 3

$- 3$ by

2

$2$ .

\frac{a^{2} + 2 a^{2} + 4 a - 3 a - 6}{a (a - 2)} \cdot \frac{a - 2}{2 a - 3}

$\frac{a^{2} + 2 a^{2} + 4 a - 3 a - 6}{a (a - 2)} \cdot \frac{a - 2}{2 a - 3}$

\frac{a^{2} + 2 a^{2} + 4 a - 3 a - 6}{a (a - 2)} \cdot \frac{a - 2}{2 a - 3}

$\frac{a^{2} + 2 a^{2} + 4 a - 3 a - 6}{a (a - 2)} \cdot \frac{a - 2}{2 a - 3}$

Step 1.2.2

Subtract

3 a

$3 a$ from

4 a

$4 a$ .

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

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

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

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

Step 1.3

Add

a^{2}

$a^{2}$ and

2 a^{2}

$2 a^{2}$ .

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

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

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

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

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of

a - 2

$a - 2$ .

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Step 2.1.1

Factor

a - 2

$a - 2$ out of

a (a - 2)

$a (a - 2)$ .

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

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

Step 2.1.2

Cancel the common factor.

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

Step 2.1.3

Rewrite the expression.

$\frac{3 a^{2} + a - 6}{a} \cdot \frac{1}{2 a - 3}$

Step 2.2

Multiply

$\frac{3 a^{2} + a - 6}{a}$ by

$\frac{1}{2 a - 3}$ .

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