1. ## simplify

Question is simplify the following expression

1 _ 1
x+2 x+4

2. Originally Posted by kiwisa
Question is simplify the following expression

1 _ 1
x+2 x+4
I assume the expression is $\displaystyle {\frac{1}{x + 2} + \frac{1}{x + 4}}$.

First try to tell me this: How you would simplify $\displaystyle {\frac{1}{3} + \frac{1}{5}}$ ? Show every step.

3. sorry but the minus sign merged with the line in the fraction so it is the 2 fractions minus each other.

1/3 + 1/5

1x5/3x5 +1x3/5x3

5/15 + 3/15

8/15

4. Originally Posted by kiwisa
sorry but the minus sign merged with the line in the fraction so it is the 2 fractions minus each other.

1/3 + 1/5

1x5/3x5 +1x3/5x3

5/15 + 3/15

8/15
Good. Now try to do the same thing with the expression you posted (but use a minus sign). Show every step.

5. 1/x+2 - 1/x+4

1x2/x+2x2 - 1/x+4

2/x+4 - 1/x+4

1/x+4

6. Originally Posted by kiwisa
1/x+2 - 1/x+4

1x2/x+2x2 - 1/x+4

2/x+4 - 1/x+4

1/x+4
That's not valid! x + 2 can be thought of as a single number that is dividing into 1, and if you are multiplying the 2 by 2, you have to multiply the x by 2 as well.

$2(x + 2) = x2 + 4$

Maybe if you substituted x + 2 and x + 4 as a single variable, you will see how your method was wrong and you will also see the correct way to solve this problem:
$j = x + 2$
$v = x + 4$
$\frac{1}{j} - \frac{1}{v}$
Simplify this just like you did the example, and at the end, put in the true values of j and v back in.

7. Now I am really lost, I can see what you are saying regarding the whole fraction been multiplied so it should read 2/2x+4, but then what?

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

x + 4 / (x^2 + 6x + 8) - [ x + 2 / (x^2 + 6x + 8) ]

[x + 4 - ( x + 2 )] / x^2 + 6x + 8

2 / x^2 + 6x + 8

9. ok so where does the 6x come from? I can see where the x^2 and the 8 come from. Sorry i just dont get this stuff.

10. It comes from FOILing (x + 4)(x + 2):
$(x + 4)(x + 2) = x^2 + 2x + 4x + 8 = x^2 + 6x + 8$

11. ( x + 4 ) ( x + 2 )

X x X + X x 2 + X x 4 + 8

x ^ 2 + 2x + 4x + 8

x ^ 2 + 6x + 8

12. Thanks i get that now

13. Originally Posted by Zharif93
1 / x+4(x+2) - 1 /x+2(x+4)

x + 4 / (x^2 + 6x + 8) - [ x + 2 / (x^2 + 6x + 8) ]

[x + 4 - ( x + 2 )] / x^2 + 6x + 8

2 / x^2 + 6x + 8
I think you meant:

(x + 4)/(x+4)(x+2) - (x + 2)/(x+2)(x+4)

= (x + 4)/ (x^2 + 6x + 8) - [(x + 2) / (x^2 + 6x + 8) ]

= [x + 4 - ( x + 2 )] /(x^2 + 6x + 8)

= 2 / (x^2 + 6x + 8)