Question

What is the simplified form of :

Answer 1

\[\frac{ x^2 - 49 }{ x^2 - 14x + 49 }\]

Answer 2

Show steps please and/or explain how to do this, I am reviewing some material and I forgot how to do this.

Answer 3

factor the top and bottom
cancel any like terms

Answer 4

the top is a "difference of squares"
it factors this way
a^2 - b^2 = (a-b)(a+b)

Answer 5

Ok so it would be:

\[\frac{ (x - 7) (x + 7) }{ x^2 - 14x + 49 }\]

Answer 6

for the bottom
first list the pairs of factors of 49:
1,49
7,7

are all of them
the + on +49 means the factors are the same sign

the -14 from -14x
means : the - means the largest factor is -. (so here both factors will be -)

now look at the pairs. which pair, with both numbers being minus, add up to -14

those will be the factors

Answer 7

Well it would be -7 and -7 because if you add both those you get -14 but if you multiply two negatives you get a positive.

Answer 8

So now I would have:

\[\frac{ (x + 7) (x-7) }{ (x-7) (x-7) }\]

Answer 9

Right?

Answer 10

yes,

now cancel (x-7) from top and bottom (because anything divided by itself is 1)

also, to be complete, make a note: x≠7 (x is not allowed to by 7)

Answer 11

Oh ok so now I would get:

\[\frac{ x + 7 }{ x - 7}\]

Answer 12

So that would be the simplified form since it cannot be simplified further right?

Answer 13

yes, that is the answer

Answer 14

Woohoo :D Thanks a bunch, I had forgotten how to do this