Question

Express x/3-1/x^2/3-3 in simplest form.

Answer 1

\[\frac{ x }{ 3 }-1\div \frac{ x ^{2} }{ 3 }-3\]

Answer 2

Still no. Use parentheses.

Like all division of fractions, try the old "Reciprocal and Multiply" idea.

Of course, you may have to do this first: \(\dfrac{x}{3} - 1 = \dfrac{x-3}{3}\)

Answer 3

@tkhunny. So then x=3if I'm right?

Answer 4

well you have an expression so its no use solving it...

the suggestion given is to get all terms over a common denominator

so

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

the difficulty is understanding your question is it

\[(\frac{x}{3} -1) \div (\frac{x^2}{3} - 3)\]

until that is decided, its difficult to givn you advice on how to simplify this problem

Answer 5

@campbell_st yes that is the question

Answer 6

ok... now you need a common denominator for the 2nd term

\[\frac{x^2}{3} - 3 = \frac{x^2}{3} - \frac{9}{3} = \frac{x^2 - 9}{3}\]

so your problem becomes

\[\frac{x -3}{3} \div \frac{x^2 - 9}{3}\]

the rule for dividing by a fraction.. in simple terms is flip and multiply

so the problem becomes

\[\frac{x -3}{3} \times \frac{3}{x^2 - 9}\]

hopefully you can work from here...

and you may need to factor the new denominator to simplify the fraction.

Answer 7

@campbell_st
So after i do that it would look like this
\[\frac{ x-3}{ 3 } * \frac{ 3 }{ x ^{2}-9 }\]

and after I do that it would lead to this
\[3*\frac{ 3 }{ x+3 }\rightarrow \frac{ 9 }{ x+3}\]

Would this be right?

Answer 8

not quite

the 3's will cancel and you are left with

\[\frac{x - 3}{3} \times \frac{3}{x^2 - 9} = \frac{x - 3}{x^2 - 9}\]

as I said before, factor the denominator and you will find another common factor that can be removed

Answer 9

So then it would be \[\frac{ x+3 }{ x-3 }\]

Answer 10

@campbell_st

Answer 11

not quite, what is the factored form of

\[x^2 - 9\]

Answer 12

\[(x-3) (x+3)\]

Answer 13

great so your problem is now

\[\frac{(x -3)}{x^2-9} = \frac{(x -3)}{(x -3)(x+3)}\]

now remove the common factor for your answer

Answer 14

oh ok so then the answer would be (x+3)

Answer 15

no... remember it's a fraction, it needs a numerator given the denominator is (x + 3)