Simplify (2/(x-3)-3/x)/(3/(x-3))

$\frac{\frac{2}{x - 3} - \frac{3}{x}}{\frac{3}{x - 3}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(\frac{2}{x - 3} - \frac{3}{x}) \frac{x - 3}{3}$

Step 2

To write $\frac{2}{x - 3}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$(\frac{2}{x - 3} \cdot \frac{x}{x} - \frac{3}{x}) \frac{x - 3}{3}$

Step 3

To write $- \frac{3}{x}$ as a fraction with a common denominator, multiply by $\frac{x - 3}{x - 3}$ .

$(\frac{2}{x - 3} \cdot \frac{x}{x} - \frac{3}{x} \cdot \frac{x - 3}{x - 3}) \frac{x - 3}{3}$

Step 4

Write each expression with a common denominator of $(x - 3) x$ , by multiplying each by an appropriate factor of $1$ .

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

$(\frac{2 x}{(x - 3) x} - \frac{3}{x} \cdot \frac{x - 3}{x - 3}) \frac{x - 3}{3}$

Multiply $\frac{3}{x}$ by $\frac{x - 3}{x - 3}$ .

$(\frac{2 x}{(x - 3) x} - \frac{3 (x - 3)}{x (x - 3)}) \frac{x - 3}{3}$

Reorder the factors of $(x - 3) x$ .

$(\frac{2 x}{x (x - 3)} - \frac{3 (x - 3)}{x (x - 3)}) \frac{x - 3}{3}$

Step 5

Combine the numerators over the common denominator.

$\frac{2 x - 3 (x - 3)}{x (x - 3)} \cdot \frac{x - 3}{3}$

Step 6

Simplify the numerator.

Apply the distributive property.

$\frac{2 x - 3 x - 3 \cdot - 3}{x (x - 3)} \cdot \frac{x - 3}{3}$

Multiply $- 3$ by $- 3$ .

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

Subtract $3 x$ from $2 x$ .

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

Step 7

Simplify terms.

Cancel the common factor of $x - 3$ .

Factor $x - 3$ out of $x (x - 3)$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{- x + 9}{x} \cdot \frac{1}{3}$

Multiply $\frac{- x + 9}{x}$ by $\frac{1}{3}$ .

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

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

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

Factor $- 1$ out of $- x$ .

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

Rewrite $9$ as $- 1 (- 9)$ .

$\frac{- (x) - 1 (- 9)}{3 x}$

Factor $- 1$ out of $- (x) - 1 (- 9)$ .

$\frac{- (x - 9)}{3 x}$

Simplify the expression.

Rewrite $- (x - 9)$ as $- 1 (x - 9)$ .

$\frac{- 1 (x - 9)}{3 x}$

Move the negative in front of the fraction.

$- \frac{x - 9}{3 x}$

Simplify (2/(x-3)-3/x)/(3/(x-3))

Related Questions

Support LCMGCF.com by disabling your adblocker.