Basic Math Examples

$\frac{2 a^{2 + 10 a}}{3 a^{2 + 15 a}}$

Step 1

Cancel the common factor of $a^{2 + 10 a}$ and $a^{2 + 15 a}$ .

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Step 1.1

Factor $a^{2 + 15 a}$ out of $2 a^{2 + 10 a}$ .

$\frac{a^{2 + 15 a} (2 a^{2 + 10 a - (2 + 15 a)})}{3 a^{2 + 15 a}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $a^{2 + 15 a}$ out of $3 a^{2 + 15 a}$ .

$\frac{a^{2 + 15 a} (2 a^{2 + 10 a - (2 + 15 a)})}{a^{2 + 15 a} \cdot 3}$

Step 1.2.2

Cancel the common factor.

$\frac{a^{2 + 15 a} (2 a^{2 + 10 a - (2 + 15 a)})}{a^{2 + 15 a} \cdot 3}$

Step 1.2.3

Rewrite the expression.

$\frac{2 a^{2 + 10 a - (2 + 15 a)}}{3}$

Step 2

Simplify the numerator.

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$\frac{2 a^{2 + 10 a - 1 \cdot 2 - (15 a)}}{3}$

Step 2.1.2

Multiply $- 1$ by $2$ .

$\frac{2 a^{2 + 10 a - 2 - (15 a)}}{3}$

Step 2.1.3

Multiply $15$ by $- 1$ .

$\frac{2 a^{2 + 10 a - 2 - 15 a}}{3}$

Step 2.2

Combine the opposite terms in $2 + 10 a - 2 - 15 a$ .

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Step 2.2.1

Subtract $2$ from $2$ .

$\frac{2 a^{10 a + 0 - 15 a}}{3}$

Step 2.2.2

Add $10 a$ and $0$ .

$\frac{2 a^{10 a - 15 a}}{3}$

Step 2.3

Subtract $15 a$ from $10 a$ .

$\frac{2 a^{- 5 a}}{3}$