Simplify (3/x+2/(x^2))/(9/(x^2)-4/x)

$\frac{\frac{3}{x} + \frac{2}{x^{2}}}{\frac{9}{x^{2}} - \frac{4}{x}}$

Step 1

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

Multiply $\frac{\frac{3}{x} + \frac{2}{x^{2}}}{\frac{9}{x^{2}} - \frac{4}{x}}$ by $\frac{x^{2}}{x^{2}}$ .

$\frac{x^{2}}{x^{2}} \cdot \frac{\frac{3}{x} + \frac{2}{x^{2}}}{\frac{9}{x^{2}} - \frac{4}{x}}$

Combine.

$\frac{x^{2} (\frac{3}{x} + \frac{2}{x^{2}})}{x^{2} (\frac{9}{x^{2}} - \frac{4}{x})}$

Step 2

Apply the distributive property.

$\frac{x^{2} \frac{3}{x} + x^{2} \frac{2}{x^{2}}}{x^{2} \frac{9}{x^{2}} + x^{2} (- \frac{4}{x})}$

Step 3

Simplify by cancelling.

Cancel the common factor of $x$ .

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

$\frac{x \cdot x \frac{3}{x} + x^{2} \frac{2}{x^{2}}}{x^{2} \frac{9}{x^{2}} + x^{2} (- \frac{4}{x})}$

Cancel the common factor.

$\frac{x \cdot x \frac{3}{x} + x^{2} \frac{2}{x^{2}}}{x^{2} \frac{9}{x^{2}} + x^{2} (- \frac{4}{x})}$

Rewrite the expression.

$\frac{x \cdot 3 + x^{2} \frac{2}{x^{2}}}{x^{2} \frac{9}{x^{2}} + x^{2} (- \frac{4}{x})}$

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

Cancel the common factor.

$\frac{x \cdot 3 + x^{2} \frac{2}{x^{2}}}{x^{2} \frac{9}{x^{2}} + x^{2} (- \frac{4}{x})}$

Rewrite the expression.

$\frac{x \cdot 3 + 2}{x^{2} \frac{9}{x^{2}} + x^{2} (- \frac{4}{x})}$

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

Cancel the common factor.

$\frac{x \cdot 3 + 2}{x^{2} \frac{9}{x^{2}} + x^{2} (- \frac{4}{x})}$

Rewrite the expression.

$\frac{x \cdot 3 + 2}{9 + x^{2} (- \frac{4}{x})}$

Cancel the common factor of $x$ .

Move the leading negative in $- \frac{4}{x}$ into the numerator.

$\frac{x \cdot 3 + 2}{9 + x^{2} \frac{- 4}{x}}$

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

$\frac{x \cdot 3 + 2}{9 + x \cdot x \frac{- 4}{x}}$

Cancel the common factor.

$\frac{x \cdot 3 + 2}{9 + x \cdot x \frac{- 4}{x}}$

Rewrite the expression.

$\frac{x \cdot 3 + 2}{9 + x \cdot - 4}$

Step 4

Move $3$ to the left of $x$ .

$\frac{3 x + 2}{9 + x \cdot - 4}$

Step 5

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

$\frac{3 x + 2}{9 - 4 x}$