Finite Math Examples

$\frac{x^{2 + 6}}{x^{2 + 4 x - 12}} + \frac{7 x}{x^{2 + 7 x + 6}}$

Step 1

Add $2$ and $6$ .

$\frac{x^{8}}{x^{2 + 4 x - 12}} + \frac{7 x}{x^{2 + 7 x + 6}}$

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $x^{8}$ and $x^{2 + 4 x - 12}$ .

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Step 2.1.1

Factor $x^{2 + 4 x - 12}$ out of $x^{8}$ .

$\frac{x^{2 + 4 x - 12} x^{8 - (2 + 4 x - 12)}}{x^{2 + 4 x - 12}} + \frac{7 x}{x^{2 + 7 x + 6}}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Multiply by $1$ .

$\frac{x^{2 + 4 x - 12} x^{8 - (2 + 4 x - 12)}}{x^{2 + 4 x - 12} \cdot 1} + \frac{7 x}{x^{2 + 7 x + 6}}$

Step 2.1.2.2

Cancel the common factor.

$\frac{x^{2 + 4 x - 12} x^{8 - (2 + 4 x - 12)}}{x^{2 + 4 x - 12} \cdot 1} + \frac{7 x}{x^{2 + 7 x + 6}}$

Step 2.1.2.3

Rewrite the expression.

$\frac{x^{8 - (2 + 4 x - 12)}}{1} + \frac{7 x}{x^{2 + 7 x + 6}}$

Step 2.1.2.4

Divide $x^{8 - (2 + 4 x - 12)}$ by $1$ .

$x^{8 - (2 + 4 x - 12)} + \frac{7 x}{x^{2 + 7 x + 6}}$

Step 2.2

Simplify each term.

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Step 2.2.1

Subtract $12$ from $2$ .

$x^{8 - (4 x - 10)} + \frac{7 x}{x^{2 + 7 x + 6}}$

Step 2.2.2

Apply the distributive property.

$x^{8 - (4 x) - - 10} + \frac{7 x}{x^{2 + 7 x + 6}}$

Step 2.2.3

Multiply $4$ by $- 1$ .

$x^{8 - 4 x - - 10} + \frac{7 x}{x^{2 + 7 x + 6}}$

Step 2.2.4

Multiply $- 1$ by $- 10$ .

$x^{8 - 4 x + 10} + \frac{7 x}{x^{2 + 7 x + 6}}$

Step 2.3

Add $8$ and $10$ .

$x^{- 4 x + 18} + \frac{7 x}{x^{2 + 7 x + 6}}$

Step 2.4

Add $2$ and $6$ .

$x^{- 4 x + 18} + \frac{7 x}{x^{7 x + 8}}$

Step 3

To write $x^{- 4 x + 18}$ as a fraction with a common denominator, multiply by $\frac{x^{7 x + 8}}{x^{7 x + 8}}$ .

$\frac{x^{- 4 x + 18} x^{7 x + 8}}{x^{7 x + 8}} + \frac{7 x}{x^{7 x + 8}}$

Step 4

Combine the numerators over the common denominator.

$\frac{x^{- 4 x + 18} x^{7 x + 8} + 7 x}{x^{7 x + 8}}$

Step 5

Multiply $x^{- 4 x + 18}$ by $x^{7 x + 8}$ by adding the exponents.

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Step 5.1

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

$\frac{x^{- 4 x + 18 + 7 x + 8} + 7 x}{x^{7 x + 8}}$

Step 5.2

Add $- 4 x$ and $7 x$ .

$\frac{x^{3 x + 18 + 8} + 7 x}{x^{7 x + 8}}$

Step 5.3

Add $18$ and $8$ .

$\frac{x^{3 x + 26} + 7 x}{x^{7 x + 8}}$