gfc. help urgent

[nemospike]

ok im getting desperate i dont know what to do on this problem and was wondering if anybody coluld help me with a problem.the math labs are closed on the weekends. this isnt home work its a practice problem and i cant move on withthe rest of the problems until i under stant

1. The problem statement, all variables and given/known data
the dircetions are to simlify:

( (b/a) - (a/b) )
--------------
( (1/a) - (1/b) )


2. Relevant equations
i undersatand the problem

( (2/x + 3) - (2/a+3) )
-------------------------
x-a

and i get how the answer is -( 2/ (x+3)(a+3) )



3. The attempt at a solution
so first i would rationzlie the nuemarator (ab -ab/(ab))
after that im lost. not sure if ab-ab would canncel and turn the numerator into 0/ab if so it would be


ive tried abunch on paper i wish i had a camera

[foxjwill]

Attempt at solution?

[nemospike]

i did. i updated the main post.

[nemospike]

please help im freaking out.....

[nemospike]

would i have to foil that ?

[njama]

Do you need to simplify the following expression:
\frac{\frac{b}{a} - \frac{a}{b}}{\frac{1}{a} - \frac{1}{b}}

Think this way. What do you need to make to get same denominator in the fractions of the original fraction? :smile:

For example, you got the following expression
\frac{x}{y}-\frac{y}{x}
now by multiplying with \frac{x}{x} for the first one, and \frac{y}{y} for the second one, what do you get?

Hint:
\frac{x}{y}\cdot \frac{x}{x} - \frac{y}{x} \cdot \frac{y}{y} :smile:

[nemospike]

i get your example perfectly. thats why i included the relevent problem and i got that answer my self. i get the easy gfc just not this hard one if you could walk me through it but when i multiply b/a *b/b and the second a/b * a/a would i get b^2 - a^2/ab

and i dont get how the answer to the enitre problem is a+b

[njama]

i get your example perfectly. thats why i included the relevent problem and i got that answer my self. i get the easy gfc just not this hard one if you could walk me through it but when i multiply b/a *b/b and the second a/b * a/a would i get b^2 - a^2/ab

and i dont get how the answer to the enitre problem is a+b

No, you would get:

\frac{b^2}{ab}-\frac{a^2}{ab}

Its obvious that the denominator of both fractions is same. What is the next step?

[nemospike]

thats what i ment . i didint mean to imply that the ab was only under the a2.im not sure on the next step. i am fuzzy on my math right now i haven't taken it in a year.i would think , i would multiply the
b2 - a2 ) a - b
-- --- * -- --
ab ab 1 1


is this even the right next step? im not sure im asking im not getting a grade on this ! can you plz just show me.

[symbolipoint]

Let me help just so much. Some of the steps are obscure in earlier posts because of the machine I am currently using.

Multiply the original expression by 1 in the form of (ab)/(ab).

[(ab)/(ab)][[(b/a)-(a/b) ]/[(1/a)-(1/b)]]=(b^2 - a^2)/(b-a)

The rest of the simplification steps should be simple.

[Mentallic]

Simplify:
( (b/a) - (a/b) )
--------------
( (1/a) - (1/b) )

ok you should go about it like this:

First, take the numerator on its own:

\frac{b}{a}-\frac{a}{b}

and manipulate these two fractions to make it all one fraction, as you've already done.

Now, take the denominator:

\frac{1}{a}-\frac{1}{b}

and again manipulate in the same fashion.

Now what you have is this fraction in the numerator and fraction in the denominator of the entire fraction, such as this:

\frac{x/y}{a/b}

And now use the rule that \frac{x}{y}\div \frac{a}{b} = \frac{x}{y} * \frac{b}{a}

All that happened was the second fraction (in the denominator of the orginal fraction) was flipped around (called taking the reciprocal) and now we can multiply rather than divide.

[HallsofIvy]

ok im getting desperate i dont know what to do on this problem and was wondering if anybody coluld help me with a problem.the math labs are closed on the weekends. this isnt home work its a practice problem and i cant move on withthe rest of the problems until i under stant

1. The problem statement, all variables and given/known data
the dircetions are to simlify:

( (b/a) - (a/b) )
--------------
( (1/a) - (1/b) )
Multiply both numerator and denomintor by the common denominator, ab:
\frac{\frac{b}{a}- \frac{a}{b}}{\frac{1}{a}- \frac{1}{b}}= \frac{b^2- a^2}{b- a}

Now use the fact that b^2- a^2= (b- a)(b+ a).


2. Relevant equations
i undersatand the problem

( (2/x + 3) - (2/a+3) )
-------------------------
x-a

and i get how the answer is -( 2/ (x+3)(a+3) )



3. The attempt at a solution
so first i would rationzlie the nuemarator (ab -ab/(ab))
after that im lost. not sure if ab-ab would canncel and turn the numerator into 0/ab if so it would be


ive tried abunch on paper i wish i had a camera