How do I simplify these four fractions?

Question

Question 1: 2x+8

------------

x+4

Question 2: x^2-y^2

---------------

x+y

Question 3: a^2-2ab+b^2

---------------------

a+b

Question 4: 2x^2+x-6

---------------------

2x+4

I'm really not trying to get someone to do my homework for me, I just really don't have a clue as to how to simplify fractions. Will someone please help!

Answer 1

this skill is very helpful when it come to limits.

simply factor the numerator, and usually you will be able to cancel out the denominator because it will most likely be one of the factors.

Answer 2

The idea is to try to factor the numerator to find something similar to the denominator.

I'll help you get start.

1. The denominator is x+4. So we need to try to find a factor like that in the numberator.

In this case 2x+8 we can factor out the 2, so we got 2(x+4).

Now we have x+4 on top and on the bottom, so we can cancel them out.

2(x+4)    

--------- = 2

(x+4)      

2. ok, so the top is now a little more harder, but does it look familiar to you? It is the difference of squares!

x^2 - y^2 = (x+y)(x-y)

There! we have the (x+y) factor, so we can cancel them out...

Answer: x-y

So now I let you try #3 and 4.

[Edit] Look like others already answer them... =P

Answer 3

the short answer: factor everything as much as possible, and then realize that any common terms will reduce to 1 (cancel, if you will)

1.  (2x + 8) / (x + 4) = 2(x + 4) / (x + 4)

note that (x + 4) / (x + 4) = 1, leaving 2*1 = 2

so this reduces to 2

2.  (x^2 - y^2) / (x + y) = (x + y) (x - y) / (x + y)

(x + y) / (x + y) = 1, leaving (x - y)

3.  (a^2 - 2ab + b^2) / (a + b) = (a - b)^2 / (a + b)

this doesn't reduce any

4)  (2x^2 + x - 6) / (2x + 4) = (2x - 3)(x + 2) / [2(x + 2)]

reduces to (2x - 3) / 2, or x - (3/2)

again, to simplify fraction like this, factor everything as much as possible and look for common factors to cancel...

Answer 4

I really don't understand what you're getting at. But here are all of the problems simplified.

1. 2X+8 = 2*(X+4)

2. X^2-Y^2 = (X+Y)*(X-Y)

3. A^2-2AB+B^2 = (A-B)*(A-B)

4. 2X^2 +X -6 = (X+2)*(2X-3)

Answer 5

These can be tough but if you'll first factor them they almost simplify themselves:

1. 2x+8 / x+4

Since 2x+8 = 2(x+4) this is really

2(x+4) / (x+4) and you can see how the x+4 equal 1, so the answer is: 2

2. x^2-y^2 / x+y

Since x^2-y^2 = (x+y)(x-y) this is really

(x+y)(x-y) and again the (x+y) cancel to get: x-y

3. All you can do with this one is factor the top and you're left with:

(a-b)^2 / (a+b)

4. The top factors to (2x-3)(x+2) and the bottom factors to 2(x+2) and you can see how the (x+2) cancels and you're left with: 2x-3 / 2

Have a good day!