How do you simplify $\frac{\frac{9}{x} - 3}{\frac{1}{3} - \frac{1}{x}}$ $\frac { \frac { 9} { x } - 3} { \frac { 1} { 3} - \frac { 1} { x } }$ ?

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Answer 1 · 2016-11-30T05:45:05

$- 9$ $-9$

You can't have fractions within a fraction. First, you must combine them in the numerator and denominator by finding common factors:

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

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

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

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

When you divide a fraction by another fraction, it is the same thing as multiplying by the second's reciprocal.

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

You can take out a common factorof -3 in the first numerator and cancel out the $x$ $x$ s of the left denominator and right numerator.

$\frac{- 3 x + 9}{x} \cdot \frac{3 x}{x - 3}$ $(-3x+9)/color(red)x*(3color(red)x)/(x-3)$

$-3cancel((x-3))*(3)/cancel((x-3))$

$=-9$

How do you simplify \frac { \frac { 9} { x } - 3} { \frac { 1} { 3} - \frac { 1} { x } }9x−313−1x\frac { \frac { 9} { x } - 3} { \frac { 1} { 3} - \frac { 1} { x } }?