Basic Math Examples

(3 a b^{2} - 5 a^{2} b + 7 a^{2} b^{2}) \div a^{2} b^{2}

$(3 a b^{2} - 5 a^{2} b + 7 a^{2} b^{2}) \div a^{2} b^{2}$

Step 1

Factor

a b

$a b$ out of

3 a b^{2} - 5 a^{2} b + 7 a^{2} b^{2}

$3 a b^{2} - 5 a^{2} b + 7 a^{2} b^{2}$ .

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Step 1.1

Factor

a b

$a b$ out of

3 a b^{2}

$3 a b^{2}$ .

(a b (3 b) - 5 a^{2} b + 7 a^{2} b^{2}) \div a^{2} b^{2}

$(a b (3 b) - 5 a^{2} b + 7 a^{2} b^{2}) \div a^{2} b^{2}$

Step 1.2

Factor

a b

$a b$ out of

- 5 a^{2} b

$- 5 a^{2} b$ .

(a b (3 b) + a b (- 5 a) + 7 a^{2} b^{2}) \div a^{2} b^{2}

$(a b (3 b) + a b (- 5 a) + 7 a^{2} b^{2}) \div a^{2} b^{2}$

Step 1.3

Factor

a b

$a b$ out of

7 a^{2} b^{2}

$7 a^{2} b^{2}$ .

(a b (3 b) + a b (- 5 a) + a b (7 a b)) \div a^{2} b^{2}

$(a b (3 b) + a b (- 5 a) + a b (7 a b)) \div a^{2} b^{2}$

Step 1.4

Factor

a b

$a b$ out of

a b (3 b) + a b (- 5 a)

$a b (3 b) + a b (- 5 a)$ .

(a b (3 b - 5 a) + a b (7 a b)) \div a^{2} b^{2}

$(a b (3 b - 5 a) + a b (7 a b)) \div a^{2} b^{2}$

Step 1.5

Factor

a b

$a b$ out of

a b (3 b - 5 a) + a b (7 a b)

$a b (3 b - 5 a) + a b (7 a b)$ .

a b (3 b - 5 a + 7 a b) \div a^{2} b^{2}

$a b (3 b - 5 a + 7 a b) \div a^{2} b^{2}$

a b (3 b - 5 a + 7 a b) \div a^{2} b^{2}

$a b (3 b - 5 a + 7 a b) \div a^{2} b^{2}$

Step 2

Reduce the expression

a b (3 b - 5 a + 7 a b) \div a^{2} b^{2}

$a b (3 b - 5 a + 7 a b) \div a^{2} b^{2}$ by cancelling the common factors.

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Step 2.1

Factor

a

$a$ out of

a b (3 b - 5 a + 7 a b)

$a b (3 b - 5 a + 7 a b)$ .

a (b (3 b - 5 a + 7 a b)) \div a^{2} b^{2}

$a (b (3 b - 5 a + 7 a b)) \div a^{2} b^{2}$

Step 2.2

Factor

a

$a$ out of

a^{2} b^{2}

$a^{2} b^{2}$ .

a (b (3 b - 5 a + 7 a b)) \div a (a b^{2})

$a (b (3 b - 5 a + 7 a b)) \div a (a b^{2})$

Step 2.3

Cancel the common factor.

a (b (3 b - 5 a + 7 a b)) \div a (a b^{2})

$a (b (3 b - 5 a + 7 a b)) \div a (a b^{2})$

Step 2.4

Rewrite the expression.

\frac{b (3 b - 5 a + 7 a b)}{a b^{2}}

$\frac{b (3 b - 5 a + 7 a b)}{a b^{2}}$

\frac{b (3 b - 5 a + 7 a b)}{a b^{2}}

$\frac{b (3 b - 5 a + 7 a b)}{a b^{2}}$

Step 3

Reduce the expression

\frac{b (3 b - 5 a + 7 a b)}{a b^{2}}

$\frac{b (3 b - 5 a + 7 a b)}{a b^{2}}$ by cancelling the common factors.

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Step 3.1

Factor

b

$b$ out of

a b^{2}

$a b^{2}$ .

\frac{b (3 b - 5 a + 7 a b)}{b (a b)}

$\frac{b (3 b - 5 a + 7 a b)}{b (a b)}$

Step 3.2

Cancel the common factor.

\frac{b (3 b - 5 a + 7 a b)}{b (a b)}

$\frac{b (3 b - 5 a + 7 a b)}{b (a b)}$

Step 3.3

Rewrite the expression.

\frac{3 b - 5 a + 7 a b}{a b}

$\frac{3 b - 5 a + 7 a b}{a b}$

\frac{3 b - 5 a + 7 a b}{a b}

$\frac{3 b - 5 a + 7 a b}{a b}$