Simplify this easy algebra equation?

(2p² - 12pq)/6p²

Factor the numerator and denominator:
2p(p - 6q)/(2p)(3p)

Cancel 2p in numerator and denominator:
(p - 6q)/3p



x² + 7x + 10/x + 2

Factor out 1/x:
(1/x)(x^3 + 7x^2 + 10 + 2x)

Rearrange:
(1/x)(x^3 + 7x^2 + 2x + 10)

Same as:
(x^3 + 7x^2 + 2x + 10)/x

The numerator cannot be factored any more, it is prime.


OR

(x² + 7x + 10)/(x + 2)

Factor the numerator:
(x + 5)(x + 2)/(x + 2)

Cancel (x + 2) in the numerator and denominator:
x + 5

Simplified: 9n-7 Pemdas. Simmppllee.

1)
(2p^2 - 12pq)/6p^2
= 2p(p - 6q)/2p(3p)
= (p - 6q)/3p
= p/3p - 6q/3p
= 1/3 - 2q/p

2)
(x^2 + 7x + 10)/(x + 2)
= (x^2 + 5x + 2x + 10)/(x + 2)
= [(x^2 + 5x) + (2x + 10)]/(x + 2)
= [x(x + 5) + 2(x + 5)]/(x + 2)
= (x + 2)(x + 5)/(x + 2)
= (x + 5)/1
= x + 5

Question 1

2p (p - 6q)
----------------
6p²

(p - 6q)
------------
3p

Question 2
Suppose you learn nothing else today, learn how to present a question properly.

You have written:-

x² + 7x + 10 / x + 2

But what you MEAN is :-

(x² + 7x + 10) / (x + 2) , two entirely different things.

(x + 5)(x + 2) / (x + 2)

x + 5

PS
Remember the brackets !

for the first one since there are p in both numerator and denominator we can cancel one of them out. so we are left with

(2p - 12q)/6p

Now we can cancel 2 out (p - 6q)/3p
and the simplification gives 1/3p(p - 6q)

the second we must simplify x^2 + 7x +10 first which gives
(x + 5) (x + 2). Now since there are (x + 2) in the bottom part it gets cancel out. and you're left with (x + 5)..

2p(p-6q)/ 6p2 = p-6q/3p
for the first equation... you should have noticed that 2p^2 and 12pq are both divisible by 2p so u can factor that out for 2p^2 and -12pq :)
and then u can divide 2p by 6p^2 to get 2/6 times p/p2 =1/3p and then u multiply it with p-6q to get p-6q/3p


(x+2)(x+5) / x+2 = x+5
use the FOIL method for this polynomial equation...
multiply FIRST , OUTER, IN, LAST and add everything together.
x times x = x^2, x times 5 = 5x, 2 times x = 2x, 2 times 5 = 10,
x^2 +5x+2x+10 = x^2 +7x+10.
then you should have noticed that x+2 is in the numerator and denominator of the fraction so they cancel out and you end up with just x+5!

HOPE THIS HELPED! ^^

2p(p-6q)/6p^2 = (p-6q)/3p
(x+2)(x+5)/(x+2) = (x+5)

Q#1) First what you have to do is collect like terms.
2p2/6p2 - 12pq/6p2
which will give you
1/3 - 2q/p
then subtract

(p - 6q)/3p

(2p² - 12pq)/6p²

Pull a 2 and a p out of the numerator, because you can find it in all terms there.

2p(p - 6q) / 6p²

Now you can cancel out with the denominator.

(p - 6q) / 3p

That's your final answer. See, not too difficult :)

x² + 7x + 10/x + 2

You're going to want to factor out the numerator on this one. Find two numbers that when multiplied equal 10 and when added equal 7. For this problem, these numbers are 2 and 5.

(x + 2)(x + 5) / x + 2

And, you can cancel out with the denominator! By the way, this is very common, so if you're completely lost on how to factor something look at what's in the denominator - sometimes not everything cancels, but normally at least one thing does.

x + 5

So there's the answer to your second problem :)