Question

How to simplify ((1/x)-(1/3)) / (x-3) ?

Answer 1

\[\frac{ \frac{ 1 }{ x } - \frac{ 1 }{ 3 } }{ x-3 }\]

Answer 2

-1/3x

Answer 3

But can I see the steps @jk_16

Answer 4

here is the idea:
(a/b)-(c/d)
=
(-b c+a d)/(b d)

Answer 5

do that for the top part..then do it again in the step when you divide by x-3

Answer 6

Why divide that by (bd)?

Answer 7

@jk_16

Answer 8

you multiply the denominator

Answer 9

the denominator is (x-3) though why (bd) ?

Answer 10

you have a choice
you can multiply top and bottom by \(3x\) to clear the fractions, or you can actually do the addition in the numerator and then simplify the compound fraction

Answer 11

\[\frac{ \frac{ 1 }{ x } - \frac{ 1 }{ 3 } }{ x-3 }=\frac{\frac{3-x}{3x}}{x-3}=\frac{3-x}{3x}\times \frac{1}{x-3}\]
\[=\frac{1}{3x}\times \frac{3-x}{x-3}\] and since \(\frac{3-x}{x-3}=-1\) you are left with \(-\frac{1}{3x}\)

Answer 12

How is it equal to -1? @satellite73