Simplify (4/x+1/(x^2))/(16/(x^2)-1/x)

$\frac{\frac{4}{x} + \frac{1}{x^{2}}}{\frac{16}{x^{2}} - \frac{1}{x}}$

Step 1

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

Multiply $\frac{\frac{4}{x} + \frac{1}{x^{2}}}{\frac{16}{x^{2}} - \frac{1}{x}}$ by $\frac{x^{2}}{x^{2}}$ .

$\frac{x^{2}}{x^{2}} \cdot \frac{\frac{4}{x} + \frac{1}{x^{2}}}{\frac{16}{x^{2}} - \frac{1}{x}}$

Combine.

$\frac{x^{2} (\frac{4}{x} + \frac{1}{x^{2}})}{x^{2} (\frac{16}{x^{2}} - \frac{1}{x})}$

Step 2

Apply the distributive property.

$\frac{x^{2} \frac{4}{x} + x^{2} \frac{1}{x^{2}}}{x^{2} \frac{16}{x^{2}} + x^{2} (- \frac{1}{x})}$

Step 3

Simplify by cancelling.

Cancel the common factor of $x$ .

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

$\frac{x \cdot x \frac{4}{x} + x^{2} \frac{1}{x^{2}}}{x^{2} \frac{16}{x^{2}} + x^{2} (- \frac{1}{x})}$

Cancel the common factor.

$\frac{x \cdot x \frac{4}{x} + x^{2} \frac{1}{x^{2}}}{x^{2} \frac{16}{x^{2}} + x^{2} (- \frac{1}{x})}$

Rewrite the expression.

$\frac{x \cdot 4 + x^{2} \frac{1}{x^{2}}}{x^{2} \frac{16}{x^{2}} + x^{2} (- \frac{1}{x})}$

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

Cancel the common factor.

$\frac{x \cdot 4 + x^{2} \frac{1}{x^{2}}}{x^{2} \frac{16}{x^{2}} + x^{2} (- \frac{1}{x})}$

Rewrite the expression.

$\frac{x \cdot 4 + 1}{x^{2} \frac{16}{x^{2}} + x^{2} (- \frac{1}{x})}$

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

Cancel the common factor.

$\frac{x \cdot 4 + 1}{x^{2} \frac{16}{x^{2}} + x^{2} (- \frac{1}{x})}$

Rewrite the expression.

$\frac{x \cdot 4 + 1}{16 + x^{2} (- \frac{1}{x})}$

Cancel the common factor of $x$ .

Move the leading negative in $- \frac{1}{x}$ into the numerator.

$\frac{x \cdot 4 + 1}{16 + x^{2} \frac{- 1}{x}}$

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

$\frac{x \cdot 4 + 1}{16 + x \cdot x \frac{- 1}{x}}$

Cancel the common factor.

$\frac{x \cdot 4 + 1}{16 + x \cdot x \frac{- 1}{x}}$

Rewrite the expression.

$\frac{x \cdot 4 + 1}{16 + x \cdot - 1}$

Step 4

Move $4$ to the left of $x$ .

$\frac{4 x + 1}{16 + x \cdot - 1}$

Step 5

Simplify the denominator.

Move $- 1$ to the left of $x$ .

$\frac{4 x + 1}{16 - 1 \cdot x}$

Rewrite $- 1 x$ as $- x$ .

$\frac{4 x + 1}{16 - x}$

Simplify (4/x+1/(x^2))/(16/(x^2)-1/x)

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