Trigonometry Examples

$\frac{x}{25} - \frac{x}{\frac{25}{\frac{x}{2}}}$

Step 1

Simplify each term.

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Step 1.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{x}{25} - (x \frac{\frac{x}{2}}{25})$

Step 1.2

Multiply the numerator by the reciprocal of the denominator.

$\frac{x}{25} - (x (\frac{x}{2} \cdot \frac{1}{25}))$

Step 1.3

Rewrite using the commutative property of multiplication.

$\frac{x}{25} - (\frac{1}{25} x \frac{x}{2})$

Step 1.4

Combine $\frac{1}{25}$ and $x$ .

$\frac{x}{25} - (\frac{x}{25} \cdot \frac{x}{2})$

Step 1.5

Multiply $\frac{x}{25} \cdot \frac{x}{2}$ .

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Step 1.5.1

Multiply $\frac{x}{25}$ by $\frac{x}{2}$ .

$\frac{x}{25} - \frac{x \cdot x}{25 \cdot 2}$

Step 1.5.2

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

$\frac{x}{25} - \frac{x^{1} x}{25 \cdot 2}$

Step 1.5.3

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

$\frac{x}{25} - \frac{x^{1} x^{1}}{25 \cdot 2}$

Step 1.5.4

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

$\frac{x}{25} - \frac{x^{1 + 1}}{25 \cdot 2}$

Step 1.5.5

Add $1$ and $1$ .

$\frac{x}{25} - \frac{x^{2}}{25 \cdot 2}$

Step 1.5.6

Multiply $25$ by $2$ .

$\frac{x}{25} - \frac{x^{2}}{50}$

Step 2

To write $\frac{x}{25}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{25} \cdot \frac{2}{2} - \frac{x^{2}}{50}$

Step 3

Write each expression with a common denominator of $50$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{x}{25}$ by $\frac{2}{2}$ .

$\frac{x \cdot 2}{25 \cdot 2} - \frac{x^{2}}{50}$

Step 3.2

Multiply $25$ by $2$ .

$\frac{x \cdot 2}{50} - \frac{x^{2}}{50}$

Step 4

Combine the numerators over the common denominator.

$\frac{x \cdot 2 - x^{2}}{50}$

Step 5

Factor $x$ out of $x \cdot 2 - x^{2}$ .

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Step 5.1

Factor $x$ out of $x \cdot 2$ .

$\frac{x (2) - x^{2}}{50}$

Step 5.2

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

$\frac{x (2) + x (- x)}{50}$

Step 5.3

Factor $x$ out of $x (2) + x (- x)$ .

$\frac{x (2 - x)}{50}$