Basic Math Examples

$\frac{4 x^{2}}{x^{2 - 25}} \cdot \frac{x - 5}{8 x^{2} + 12 x}$

Step 1

Simplify the denominator.

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Step 1.1

Subtract $25$ from $2$ .

$\frac{4 x^{2}}{x^{- 23}} \cdot \frac{x - 5}{8 x^{2} + 12 x}$

Step 1.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{4 x^{2}}{\frac{1}{x^{23}}} \cdot \frac{x - 5}{8 x^{2} + 12 x}$

Step 2

Simplify terms.

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Step 2.1

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

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Step 2.1.1

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

$\frac{4 x^{2}}{\frac{1}{x^{23}}} \cdot \frac{x - 5}{4 x (2 x) + 12 x}$

Step 2.1.2

Factor $4 x$ out of $12 x$ .

$\frac{4 x^{2}}{\frac{1}{x^{23}}} \cdot \frac{x - 5}{4 x (2 x) + 4 x (3)}$

Step 2.1.3

Factor $4 x$ out of $4 x (2 x) + 4 x (3)$ .

$\frac{4 x^{2}}{\frac{1}{x^{23}}} \cdot \frac{x - 5}{4 x (2 x + 3)}$

Step 2.2

Cancel the common factor of $4 x$ .

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Step 2.2.1

Factor $4 x$ out of $4 x^{2}$ .

$\frac{4 x (x)}{\frac{1}{x^{23}}} \cdot \frac{x - 5}{4 x (2 x + 3)}$

Step 2.2.2

Cancel the common factor.

$\frac{4 x \cdot x}{\frac{1}{x^{23}}} \cdot \frac{x - 5}{4 x (2 x + 3)}$

Step 2.2.3

Rewrite the expression.

$\frac{x}{\frac{1}{x^{23}}} \cdot \frac{x - 5}{2 x + 3}$

Step 2.3

Multiply $\frac{x}{\frac{1}{x^{23}}}$ by $\frac{x - 5}{2 x + 3}$ .

$\frac{x (x - 5)}{\frac{1}{x^{23}} (2 x + 3)}$

Step 3

Factor $\frac{1}{x^{23}}$ out of $\frac{x (x - 5)}{\frac{1}{x^{23}} (2 x + 3)}$ .

$x^{23} \frac{x (x - 5)}{2 x + 3}$

Step 4

Multiply $x^{23} \frac{x (x - 5)}{2 x + 3}$ .

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Step 4.1

Combine $x^{23}$ and $\frac{x (x - 5)}{2 x + 3}$ .

$\frac{x^{23} (x (x - 5))}{2 x + 3}$

Step 4.2

Multiply $x^{23}$ by $x$ by adding the exponents.

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Step 4.2.1

Move $x$ .

$\frac{x \cdot x^{23} (x - 5)}{2 x + 3}$

Step 4.2.2

Multiply $x$ by $x^{23}$ .

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Step 4.2.2.1

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

$\frac{x^{1} x^{23} (x - 5)}{2 x + 3}$

Step 4.2.2.2

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

$\frac{x^{1 + 23} (x - 5)}{2 x + 3}$

Step 4.2.3

Add $1$ and $23$ .

$\frac{x^{24} (x - 5)}{2 x + 3}$