Adding and subtracting Fraction?

Question

I have to express my answer in simplest form here is my equation

x^2
-----
x +4

+

11x +28
------------
x+4


Do I add the top line together and add the bottom line to get

x^2 +11x +28
-----------------
x^2 + 8 ????????

If so then what are the steps after this ?


Also I have to subtract this faction

5x-3
-------
6

minus

x+3
------
6


Your help is greatly appreciated ! :)

Answer 1

for the 1st part,

the denominator does not change as they are already the same (just like adding number fractions).
therefore, it becomes:

x² +11x +28
------------------
x + 4


the expression on top (the numerator) ,
x² +11x +28 can be factorised to (x+4)(x+7)

fraction becomes:

(x+4)(x+7)
------------------
x + 4

simplified, the fraction becomes (x+7).







For the second part,
again, the denominator is the same (expression at the bottom of the fraction),
therefore just subtract the numerators.

(5x-3) - (x+3)
-------------------
6


next step:

4x -6
---------
6


simplify

2 (2x-3)
----------
6


answer is:
(2x-3)
---------
3

Answer 2

ok lets take a step back real quick.

if you have two fractions with the same denominator such as 1/5 and 2/5 then you only add the numerators together and keep the denominator the same.

This means 1/5 + 2/5 = 3/5
See how the denominator of 5 stayed a 5?

Ok back to the algebra problem

x^2
-----
x +4

+

11x +28
------------
x+4

Both fractions have a denominator of x + 4 so the denominator stays x+4. This means you only have to add the numberators. This leaves you with:

x^2 +11x +28
-------------------
x + 4

Now you wanna make sure this is in simplest form. This means you need to see if x^2 +11x +28 factors. It does factor:

x^2 +11x +28 = (x + 4)(x + 7)

(x + 4)(x + 7)
------------------
x + 4

x + 4 cancles from the numerator and denominator leaving you with x + 7 as an answer.

Answer: x + 7



Now for the second equation:

5x-3
-------
6

minus

x+3
------
6

Both equations have a denominator of 6 so the dominator stays 6 in your final answer. This means you just subtract the numerators leaving you with:

5x - 3 -(x + 3)
------------------
6

Notice how x + 3 was put in parenthesis. This is because you are subtracting the entire quantity x + 3 and not just x. Distribute the - sign onto x and 3 leaving you with:

5x - 3 -x -3
--------------
6

Combine like terms: 5x - x gives you 4x
and -3 -3 gives you -6

This leaves you with

4x - 6
--------
6

You notice on the top a 2 can be factored out of both 4x and - 6 giving you:

2(2x - 3)
------------
6

Also 6 can be factored into 2(3):

2(2x - 3)
------------
2(3)

You notice from the numerator and denominator a 2 cancels leaving you with:

2x - 3
--------
3

Answer 3

First question to add fractions together you must have (or make) the same denominator. Guess what x+4 and x+4 are the same so you get

x^2+11x+28
-------------------
x+4

factor the top (x+7)(x+4)
---------------
(x+4)

cancel the x+4 leaving x+7
method 2
do you know long division? fractions are just the top divided by the botom.
__________
x+4|x^2+11x+28

__x_______
x+4|x^2+11x+28
x^2+4x

subtract
__x_______
x+4|x^2+11x+28
x^2+4x
0+ 7x
next how many times will x+4 go into 7x+28 the answer 7
__x+7____
x+4|x^2+11x+28
x^2+4x
0+ 7x
7x+28
subtract no remander

Answer 4

1. (x^2)/(x +4) + (11x +28)/(x+4)

First: since you have the same denominators > add the numerators >

[x^2 + 11x + 28]/x+4

Sec: factor the numerator >

[(x+4)(x+7)]/x+4

Third: cancel "like" terms: cancel x+4 from the top and bottom >

x + 7

2. follow the same format as number (1)-give it a try :-)

Answer 5

In the first equation, because the denominators are the same, you just add the top and the denominator (bottom) stays the same.
Same thing with the second equation. Just subtract the top, leave the bottom. You only touch the bottom if there's a different denominator and you need to multiply them by something to make them equal.

Answer 6

These equations have common denominators so you would express it this way:

1. x^2+11x+28 (x+4)(x+7)
--------------- --------------- = x+7 Answer
x+4 x+4
2. 5x-3 x+3 4x
------- - -------- = ------------ Answer
6 6 6

Answer 7

you don't add or subtract denominator

x^2/(x+4)+(11x+28)/(x+4)= (x^2+11x+28)/(x+4)

fator out

(x+7)(x+4) / (x+4)
the x+4 cancel out

ans: x+7

samething with subtraction. you try it.