Pre-Algebra Examples

\frac{5}{x^{2} (x - 2)} + \frac{x}{x - 2}

$\frac{5}{x^{2} (x - 2)} + \frac{x}{x - 2}$

Step 1

To write

\frac{x}{x - 2}

$\frac{x}{x - 2}$ as a fraction with a common denominator, multiply by

\frac{x^{2}}{x^{2}}

$\frac{x^{2}}{x^{2}}$ .

\frac{5}{x^{2} (x - 2)} + \frac{x}{x - 2} \cdot \frac{x^{2}}{x^{2}}

$\frac{5}{x^{2} (x - 2)} + \frac{x}{x - 2} \cdot \frac{x^{2}}{x^{2}}$

Step 2

Write each expression with a common denominator of

(x - 2) x^{2}

$(x - 2) x^{2}$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 2.1

Multiply

\frac{x}{x - 2}

$\frac{x}{x - 2}$ by

\frac{x^{2}}{x^{2}}

$\frac{x^{2}}{x^{2}}$ .

\frac{5}{x^{2} (x - 2)} + \frac{x \cdot x^{2}}{(x - 2) x^{2}}

$\frac{5}{x^{2} (x - 2)} + \frac{x \cdot x^{2}}{(x - 2) x^{2}}$

Step 2.2

Reorder the factors of

(x - 2) x^{2}

$(x - 2) x^{2}$ .

\frac{5}{x^{2} (x - 2)} + \frac{x \cdot x^{2}}{x^{2} (x - 2)}

$\frac{5}{x^{2} (x - 2)} + \frac{x \cdot x^{2}}{x^{2} (x - 2)}$

\frac{5}{x^{2} (x - 2)} + \frac{x \cdot x^{2}}{x^{2} (x - 2)}

$\frac{5}{x^{2} (x - 2)} + \frac{x \cdot x^{2}}{x^{2} (x - 2)}$

Step 3

Combine the numerators over the common denominator.

\frac{5 + x \cdot x^{2}}{x^{2} (x - 2)}

$\frac{5 + x \cdot x^{2}}{x^{2} (x - 2)}$

Step 4

Multiply

x

$x$ by

x^{2}

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

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Step 4.1

Multiply

x

$x$ by

x^{2}

$x^{2}$ .

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Step 4.1.1

Raise

x

$x$ to the power of

1

$1$ .

\frac{5 + x^{1} x^{2}}{x^{2} (x - 2)}

$\frac{5 + x^{1} x^{2}}{x^{2} (x - 2)}$

Step 4.1.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

\frac{5 + x^{1 + 2}}{x^{2} (x - 2)}

$\frac{5 + x^{1 + 2}}{x^{2} (x - 2)}$

\frac{5 + x^{1 + 2}}{x^{2} (x - 2)}

$\frac{5 + x^{1 + 2}}{x^{2} (x - 2)}$

Step 4.2

Add

1

$1$ and

2

$2$ .

\frac{5 + x^{3}}{x^{2} (x - 2)}

$\frac{5 + x^{3}}{x^{2} (x - 2)}$

\frac{5 + x^{3}}{x^{2} (x - 2)}

$\frac{5 + x^{3}}{x^{2} (x - 2)}$