Simplify (25/x-x)/(2+10/x)

$\frac{\frac{25}{x} - x}{2 + \frac{10}{x}}$

Step 1

Multiply the numerator and denominator of the complex fraction by $x$ .

Multiply $\frac{\frac{25}{x} - x}{2 + \frac{10}{x}}$ by $\frac{x}{x}$ .

$\frac{x}{x} \cdot \frac{\frac{25}{x} - x}{2 + \frac{10}{x}}$

Combine.

$\frac{x (\frac{25}{x} - x)}{x (2 + \frac{10}{x})}$

Step 2

Apply the distributive property.

$\frac{x \frac{25}{x} + x (- x)}{x \cdot 2 + x \frac{10}{x}}$

Step 3

Simplify by cancelling.

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x \frac{25}{x} + x (- x)}{x \cdot 2 + x \frac{10}{x}}$

Rewrite the expression.

$\frac{25 + x (- x)}{x \cdot 2 + x \frac{10}{x}}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{25 + x (- x)}{x \cdot 2 + x \frac{10}{x}}$

Rewrite the expression.

$\frac{25 + x (- x)}{x \cdot 2 + 10}$

Step 4

Simplify the numerator.

Rewrite $25$ as $5^{2}$ .

$\frac{5^{2} + x (- x)}{x \cdot 2 + 10}$

Rewrite $x (x)$ as $x^{2}$ .

$\frac{5^{2} - x^{2}}{x \cdot 2 + 10}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 5$ and $b = x$ .

$\frac{(5 + x) (5 - x)}{x \cdot 2 + 10}$

Step 5

Simplify terms.

Factor $2$ out of $x \cdot 2 + 10$ .

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

$\frac{(5 + x) (5 - x)}{2 \cdot x + 10}$

Factor $2$ out of $10$ .

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

Factor $2$ out of $2 \cdot x + 2 \cdot 5$ .

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

Cancel the common factor of $5 + x$ and $x + 5$ .

Reorder terms.

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{5 - x}{2}$

Simplify (25/x-x)/(2+10/x)

Related Questions

Support LCMGCF.com by disabling your adblocker.