Algebra Examples

$5^{x} + 5^{x + 3} = A \cdot 5^{x}$

Step 1

Rewrite the equation as $A \cdot 5^{x} = 5^{x} + 5^{x + 3}$ .

$A \cdot 5^{x} = 5^{x} + 5^{x + 3}$

Step 2

Divide each term in $A \cdot 5^{x} = 5^{x} + 5^{x + 3}$ by $5^{x}$ and simplify.

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Step 2.1

Divide each term in $A \cdot 5^{x} = 5^{x} + 5^{x + 3}$ by $5^{x}$ .

$\frac{A \cdot 5^{x}}{5^{x}} = \frac{5^{x}}{5^{x}} + \frac{5^{x + 3}}{5^{x}}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5^{x}$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{A \cdot 5^{x}}{5^{x}} = \frac{5^{x}}{5^{x}} + \frac{5^{x + 3}}{5^{x}}$

Step 2.2.1.2

Divide $A$ by $1$ .

$A = \frac{5^{x}}{5^{x}} + \frac{5^{x + 3}}{5^{x}}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Combine the numerators over the common denominator.

$A = \frac{5^{x} + 5^{x + 3}}{5^{x}}$

Step 2.3.2

Split the fraction $\frac{5^{x} + 5^{x + 3}}{5^{x}}$ into two fractions.

$A = \frac{5^{x}}{5^{x}} + \frac{5^{x + 3}}{5^{x}}$

Step 2.3.3

Cancel the common factor of $5^{x}$ .

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Step 2.3.3.1

Cancel the common factor.

$A = \frac{5^{x}}{5^{x}} + \frac{5^{x + 3}}{5^{x}}$

Step 2.3.3.2

Rewrite the expression.

$A = 1 + \frac{5^{x + 3}}{5^{x}}$

Step 2.3.4

Cancel the common factor of $5^{x + 3}$ and $5^{x}$ .

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Step 2.3.4.1

Factor $5^{x}$ out of $5^{x + 3}$ .

$A = 1 + \frac{5^{x} \cdot 5^{3}}{5^{x}}$

Step 2.3.4.2

Cancel the common factors.

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Step 2.3.4.2.1

Multiply by $1$ .

$A = 1 + \frac{5^{x} \cdot 5^{3}}{5^{x} \cdot 1}$

Step 2.3.4.2.2

Cancel the common factor.

$A = 1 + \frac{5^{x} \cdot 5^{3}}{5^{x} \cdot 1}$

Step 2.3.4.2.3

Rewrite the expression.

$A = 1 + \frac{5^{3}}{1}$

Step 2.3.4.2.4

Divide $5^{3}$ by $1$ .

$A = 1 + 5^{3}$

Step 2.3.5

Simplify the expression.

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Step 2.3.5.1

Raise $5$ to the power of $3$ .

$A = 1 + 125$

Step 2.3.5.2

Add $1$ and $125$ .

$A = 126$