What are the steps to this problem (algebra)?

Question

[(1) - (25/x^2)] / [(1) - (8/x) + (15/x^2)]

the instructions are to "perform the indicated operations"
the answer is supposed to be:
(x+5)/(x-3)
I can't figure out how to get there.

I actually got the answer, but I'll still leave it up and give the points to whoever's answer is clearest.

Answer 1

The trick is to multiply the top and the bottom by x^2.
Then the expression becomes:
(x^2-25)/(x^2-8x+15)=[(x-5)(x+5)]/[(x-5)(x-3)].So the (x+5) cancels out and you have the answer.

Answer 2

Step 1) make all denominators = x^2. This will cancel out afterwards
[ (x^2 / x^2) - (25 / x ^ 2)] / [ (x^2 / x^2) - (8x / x^2) + (15 / x ^ 2)

Step 2) cancel X^2
[ x^2 - 25] / [ x^2 - 8x + 15]

Step 3) factorize
Step 3.1) top [ x^2 - 25] = (x - 5) * (x + 5)
you hopefully know that, since this equation has the form
(a^2 - b^2)

Step 3.2) bottom solve for
x^2 - 8x + 15 = 0
and get solution
x = 3 and x = 5
write as (x - 3) * (x - 5)

Step 4) eliminate (x-5)
[ (x - 5) * (x + 5) ] / [ (x - 3) * (x - 5) ]

Step 5) finished
(x + 5) / ( x - 3)

Answer 3

Start by simplifying the numerator and denominator:[(x^2-25)/x^2]/[(x^2-8x+15)/x^2]
now you can cancel out the x^2 that are on the bottom of both the top and bottom terms to get (x^2-25)/(x^2-8x+15)
The next step is to factor both the top and bottom to get:
[(x-5)(x+5)]/[(x-3)(x-5)]
Notice that you can now cancel the two (x-5) terms to get:
(x+5)/(x-3)

Answer 4

[(1) - (25/x^2)] / [(1) - (8/x) + (15/x^2)]

You could start by factoring both the big numerator and the big denominator as is, but it makes more sense to first multiply the big numerator and the big denominator by x^2 to clear the fractions with x^2 and x as denominators.

(x^2 - 25)/(x^2 - 8x + 15)

Now the rational expression is easy to factor

[(x + 5)(x - 5)]/[x - 3)(x - 5)

Whence yo get

(x + 5)/(x - 3)

Answer 5

PEMDAS :D EXAMPLES XP A and B=any volume :P X+A=B-X=A=B-2x (you ought to characteristic or subtract from both component depending if S grew to change into both negative or effective) 5(6x+7) distributive resources, you're taking the 5 and multiply it by skill of utilizing each and each volume contained in the parenthesis which makes 30x+35 if the / are fractions than you may want to replace them into decimals... yet at the same time as the characterize multiplication than ok... which will be sufficient to end you mission.... and questions like volume 29 the area it has -2(x+3) the area its only a variable, than you only positioned the volume infront of it...

Answer 6

muliply everything by x^2/x^2
you should get (x^2-25)/(x^2-8x+15)
factor and get [(x-5)(x+5)]/[(x-5)(x-3)]
cancel the x-5 on the top and bottom and you get (x+5)/(x-3)

Answer 7

wow
good luck!