simplyfy, x squared + 25 / 5(x-5)?

Question

and don't even bother to write ' do your homework yourself' or i'll put a fingers down for you.

Answer 1

(x^2 + 25)
-------------
5(x-5)



The first step is to look at the numerator (top) and see if you can factor it.

Set (x^2 + 25) equal to zero and solve for the roots.
(x^2 + 25) = 0
x^2 = -25

I'm not sure if you are familiar with 'imaginary numbers' yet but if you are you know that x^2 can only equal a negative number if x is an imaginary number. If you aren't familiar with them then don't worry about anything other than the fact that you can't factor it. Since there aren't any imaginary numbers in the denominator (bottom) we don't need to bother to factor (x^2 + 25).

Now let's look at the denominator: 5(x-5).
You can use the distributive law to get (5x-25)

Answer:
(x^2 + 25)
--------------
5x - 25


This is your answer in simplyfied terms. (Simplify means to express it in the fewest terms possible) I'm guessing the purpose of this problem was to see if you would fall into the pitfall of thinking (x^2 + 25) = (x+5)^2.

WARNING: (x^2 + 25) is NOT equal to (x+5)^2!
(x+5)(x+5) = x^2 + 5x + 5x + 25 = x^2+10x+25
Clearly (x^2+10x+25) is not equal to (x^2+25)

Hopefully that helps you some.

Answer 2

Stephen C. did an illegal operation by cancelling the 25's. Lizard gave you (x-5)(x+5) as a simplification of x^2+25, but it is actually a simplification of x^2-25. As far as I can see, you can only simplify your problem to 5(x^2+25)/(x-5) unless you want to use imaginary numbers. Then the answer is 5(x-5i)(x+5i)/(x-5)

Answer 3

hmmmmmmm, its been a while since i did my degree, and even longer since we did this kinda stuff in it. but i will guess..............

X^2 + 25 / 5 * (x - 5)

first times out the brackets to get:

x^2 + 25 / 5x - 25

then i beleive the +25 on the top and the -25 on the bottom will cancel one and other out, so you get

x^2 / 5x

now this is the same as x * x / 5 * x
therefore, one of the x's on the top cancel out an x on the bottom. so this takes it to x / 5

my finalal answer is x/5. but if you have to put working remember to put the bit where you expand it to x * x / 5 * x its important part.

Answer 4

There's some slight ambiguity here I assume the question is

(x^2+25)/(5(x-5))

(x-5)^2= x^2-10x+25 sp (x^2+25)=(x-5)^2+10x

So we can re-write the question as

((x-5)^2+10x)/(5(x-5))

this is

(x-5)^2/(5(x-5)+10x/(5(x-5)

=(x-5)+2x/(x-5)

Answer 5

x^2+25/5(x-5)
=
x^2 + 5/x-5
=
x^3-5X^2+5
x^3 +5 ( 5 - x^2)/x-5 = 0
and multiply by (x -5)
to get
x^3 -5x^2 + 5
now factorize with factor theorem
Sorry cannot be done no proper factor
or it can be
x^2 + 5/x-5

Answer 6

I haven't done algebra in a long time but I'm going to give ya a shot

(X-5)^2/5(x-5)... I am totally lost and I did this stuff in 6th grade.
x2-10x+25
(x-5)(x-5)-10x/5(x-5)

=(x-5)-2x

I foiled it....
x2-5x-5x+25
x2 -10x+25


Someone tell me I finally got it? Or let me know what I am doing wrong....

Answer 7

The simplified answer is X squared / 5x.

Answer 8

-5-x^2=5x x^2+5x+5=0 =-5+or-(25-20)^a million/2 ------------------------------- 2(a million) =-5+ or - sqrt(5) ------------------------ 2 =-5+sqrt5 ------------- 2 or =-5-sqrt5 ------------- 2