Finite Math Examples

$\frac{x^{2} + 2 x + 3}{x^{2 - 9}}$

Step 1

Move $x^{2 - 9}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$(x^{2} + 2 x + 3) x^{- (2 - 9)}$

Step 2

Simplify the expression.

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Step 2.1

Subtract $9$ from $2$ .

$(x^{2} + 2 x + 3) x^{- - 7}$

Step 2.2

Multiply $- 1$ by $- 7$ .

$(x^{2} + 2 x + 3) x^{7}$

Step 3

Apply the distributive property.

$x^{2} x^{7} + 2 x \cdot x^{7} + 3 x^{7}$

Step 4

Simplify.

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Step 4.1

Multiply $x^{2}$ by $x^{7}$ by adding the exponents.

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Step 4.1.1

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

$x^{2 + 7} + 2 x \cdot x^{7} + 3 x^{7}$

Step 4.1.2

Add $2$ and $7$ .

$x^{9} + 2 x \cdot x^{7} + 3 x^{7}$

Step 4.2

Multiply $x$ by $x^{7}$ by adding the exponents.

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Step 4.2.1

Move $x^{7}$ .

$x^{9} + 2 (x^{7} x) + 3 x^{7}$

Step 4.2.2

Multiply $x^{7}$ by $x$ .

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Step 4.2.2.1

Raise $x$ to the power of $1$ .

$x^{9} + 2 (x^{7} x^{1}) + 3 x^{7}$

Step 4.2.2.2

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

$x^{9} + 2 x^{7 + 1} + 3 x^{7}$

Step 4.2.3

Add $7$ and $1$ .

$x^{9} + 2 x^{8} + 3 x^{7}$