Simplify (7-7/(3x))/(5/x-5/(3x^2))

$\frac{7 - \frac{7}{3 x}}{\frac{5}{x} - \frac{5}{3 x^{2}}}$

Multiply the numerator and denominator of the complex fraction by $3 x^{2}$ .

Multiply $\frac{7 - \frac{7}{3 x}}{\frac{5}{x} - \frac{5}{3 x^{2}}}$ by $\frac{3 x^{2}}{3 x^{2}}$ .

$\frac{3 x^{2}}{3 x^{2}} \cdot \frac{7 - \frac{7}{3 x}}{\frac{5}{x} - \frac{5}{3 x^{2}}}$

Combine.

$\frac{3 x^{2} (7 - \frac{7}{3 x})}{3 x^{2} (\frac{5}{x} - \frac{5}{3 x^{2}})}$

Apply the distributive property.

$\frac{3 x^{2} \cdot 7 + 3 x^{2} (- \frac{7}{3 x})}{3 x^{2} \frac{5}{x} + 3 x^{2} (- \frac{5}{3 x^{2}})}$

Simplify by cancelling.

Cancel the common factor of $3 x$ .

Move the leading negative in $- \frac{7}{3 x}$ into the numerator.

$\frac{3 x^{2} \cdot 7 + 3 x^{2} \frac{- 7}{3 x}}{3 x^{2} \frac{5}{x} + 3 x^{2} (- \frac{5}{3 x^{2}})}$

Factor $3 x$ out of $3 x^{2}$ .

$\frac{3 x^{2} \cdot 7 + 3 x (x) \frac{- 7}{3 x}}{3 x^{2} \frac{5}{x} + 3 x^{2} (- \frac{5}{3 x^{2}})}$

Cancel the common factor.

$\frac{3 x^{2} \cdot 7 + 3 x \cdot x \frac{- 7}{3 x}}{3 x^{2} \frac{5}{x} + 3 x^{2} (- \frac{5}{3 x^{2}})}$

Rewrite the expression.

$\frac{3 x^{2} \cdot 7 + x \cdot - 7}{3 x^{2} \frac{5}{x} + 3 x^{2} (- \frac{5}{3 x^{2}})}$

Cancel the common factor of $x$ .

Factor $x$ out of $3 x^{2}$ .

$\frac{3 x^{2} \cdot 7 + x \cdot - 7}{x (3 x) \frac{5}{x} + 3 x^{2} (- \frac{5}{3 x^{2}})}$

Cancel the common factor.

$\frac{3 x^{2} \cdot 7 + x \cdot - 7}{x (3 x) \frac{5}{x} + 3 x^{2} (- \frac{5}{3 x^{2}})}$

Rewrite the expression.

$\frac{3 x^{2} \cdot 7 + x \cdot - 7}{3 x \cdot 5 + 3 x^{2} (- \frac{5}{3 x^{2}})}$

Multiply $5$ by $3$ .

$\frac{3 x^{2} \cdot 7 + x \cdot - 7}{15 x + 3 x^{2} (- \frac{5}{3 x^{2}})}$

Cancel the common factor of $3 x^{2}$ .

Move the leading negative in $- \frac{5}{3 x^{2}}$ into the numerator.

$\frac{3 x^{2} \cdot 7 + x \cdot - 7}{15 x + 3 x^{2} \frac{- 5}{3 x^{2}}}$

Cancel the common factor.

$\frac{3 x^{2} \cdot 7 + x \cdot - 7}{15 x + 3 x^{2} \frac{- 5}{3 x^{2}}}$

Rewrite the expression.

$\frac{3 x^{2} \cdot 7 + x \cdot - 7}{15 x - 5}$

Simplify terms.

Factor $x \cdot 7$ out of $3 x^{2} \cdot 7 + x \cdot - 7$ .

Factor $x \cdot 7$ out of $3 x^{2} \cdot 7$ .

$\frac{x \cdot 7 (3 x) + x \cdot - 7}{15 x - 5}$

Factor $x \cdot 7$ out of $x \cdot - 7$ .

$\frac{x \cdot 7 (3 x) + x \cdot 7 (- 1)}{15 x - 5}$

Factor $x \cdot 7$ out of $x \cdot 7 (3 x) + x \cdot 7 (- 1)$ .

$\frac{x \cdot 7 (3 x - 1)}{15 x - 5}$

Factor $5$ out of $15 x - 5$ .

Factor $5$ out of $15 x$ .

$\frac{x \cdot 7 (3 x - 1)}{5 (3 x) - 5}$

Factor $5$ out of $- 5$ .

$\frac{x \cdot 7 (3 x - 1)}{5 (3 x) + 5 (- 1)}$

Factor $5$ out of $5 (3 x) + 5 (- 1)$ .

$\frac{x \cdot 7 (3 x - 1)}{5 (3 x - 1)}$

Cancel the common factor of $3 x - 1$ .

Cancel the common factor.

$\frac{x \cdot 7 (3 x - 1)}{5 (3 x - 1)}$

Rewrite the expression.

$\frac{x \cdot 7}{5}$

Move $7$ to the left of $x$ .

$\frac{7 x}{5}$

Simplify (7-7/(3x))/(5/x-5/(3x^2))

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