Simplify (2/x+5/(x^2))/(4/(x^2)-25/x)

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

Step 1

Multiply the numerator and denominator of the complex fraction by $x^{2}$ .

Multiply $\frac{\frac{2}{x} + \frac{5}{x^{2}}}{\frac{4}{x^{2}} - \frac{25}{x}}$ by $\frac{x^{2}}{x^{2}}$ .

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

Combine.

$\frac{x^{2} (\frac{2}{x} + \frac{5}{x^{2}})}{x^{2} (\frac{4}{x^{2}} - \frac{25}{x})}$

Step 2

Apply the distributive property.

$\frac{x^{2} \frac{2}{x} + x^{2} \frac{5}{x^{2}}}{x^{2} \frac{4}{x^{2}} + x^{2} (- \frac{25}{x})}$

Step 3

Simplify by cancelling.

Cancel the common factor of $x$ .

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

$\frac{x \cdot x \frac{2}{x} + x^{2} \frac{5}{x^{2}}}{x^{2} \frac{4}{x^{2}} + x^{2} (- \frac{25}{x})}$

Cancel the common factor.

$\frac{x \cdot x \frac{2}{x} + x^{2} \frac{5}{x^{2}}}{x^{2} \frac{4}{x^{2}} + x^{2} (- \frac{25}{x})}$

Rewrite the expression.

$\frac{x \cdot 2 + x^{2} \frac{5}{x^{2}}}{x^{2} \frac{4}{x^{2}} + x^{2} (- \frac{25}{x})}$

Cancel the common factor of $x^{2}$ .

Cancel the common factor.

$\frac{x \cdot 2 + x^{2} \frac{5}{x^{2}}}{x^{2} \frac{4}{x^{2}} + x^{2} (- \frac{25}{x})}$

Rewrite the expression.

$\frac{x \cdot 2 + 5}{x^{2} \frac{4}{x^{2}} + x^{2} (- \frac{25}{x})}$

Cancel the common factor of $x^{2}$ .

Cancel the common factor.

$\frac{x \cdot 2 + 5}{x^{2} \frac{4}{x^{2}} + x^{2} (- \frac{25}{x})}$

Rewrite the expression.

$\frac{x \cdot 2 + 5}{4 + x^{2} (- \frac{25}{x})}$

Cancel the common factor of $x$ .

Move the leading negative in $- \frac{25}{x}$ into the numerator.

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Move $2$ to the left of $x$ .

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

Step 5

Move $- 25$ to the left of $x$ .

$\frac{2 x + 5}{4 - 25 x}$