(X^2 + 9)  25

X  4
(X not equal 4)
Okay I'm an idiot. I know the answer is [x + 4] but I am not sure how to arrive there.

X  4
(X not equal 4)
Okay I'm an idiot. I know the answer is [x + 4] but I am not sure how to arrive there.

Simplify the top first:
(x^2+9)25=x^216.
This is a difference of two squares. Not sure if you know what that means, so I'll give a brief explanation:
When you have something of the form x^2y^2 it factorises to (x+y)(xy).
Here we have x^216. 16 is 4^2. Therefore we can write:
x^2=4^2
Therefore, this factorises to (x+4)(x4).
The key to spotting differences of two squares it to just look out for when you have x^2 minus a square number (1,4,9,16,25 etc)
The more practice you get, the better you will become at spotting common patterns like this.
We cannot simplify the bottom half.
So, now we have (x+4)(x4)/(x4)
Cancel the factors of (x4):
(x+4)(x4) / (x4)=x+4
(x^2+9)25=x^216.
This is a difference of two squares. Not sure if you know what that means, so I'll give a brief explanation:
When you have something of the form x^2y^2 it factorises to (x+y)(xy).
Here we have x^216. 16 is 4^2. Therefore we can write:
x^2=4^2
Therefore, this factorises to (x+4)(x4).
The key to spotting differences of two squares it to just look out for when you have x^2 minus a square number (1,4,9,16,25 etc)
The more practice you get, the better you will become at spotting common patterns like this.
We cannot simplify the bottom half.
So, now we have (x+4)(x4)/(x4)
Cancel the factors of (x4):
(x+4)(x4) / (x4)=x+4

x62+925=x^216 which can factored into (x+4)(x4) so (x4) cancels out with the (x4) in the denominator of given ratio. Thus the answer is (x+4)

factored...
(x^2 + 9)  25
= x^2 + 9  25
= x^2  16 > Diffrence of a square
= (x + 4) (x  4)
(x^2 + 9)  25
= x^2 + 9  25
= x^2  16 > Diffrence of a square
= (x + 4) (x  4)