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all i know that a = 3

 Mar 31, 2019
 #1
avatar+1015 
-3

Give me a second I belive you posted this before let me look BACK

 Mar 31, 2019
 #2
avatar+1015 
-2

Yes you did post it but knowone helped

 

https://web2.0calc.com/questions/please-help_95973

Nickolas  Mar 31, 2019
 #3
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+2

Simplify the following:
2 - (x + 1)/(x - 2) - (x - 4)/(x + 2)

Put each term in 2 - (x + 1)/(x - 2) - (x - 4)/(x + 2) over the common denominator (x - 2) (x + 2): 2 - (x + 1)/(x - 2) - (x - 4)/(x + 2) = (2 (x - 2) (x + 2))/((x - 2) (x + 2)) + ((-x - 1) (x + 2))/((x - 2) (x + 2)) + ((4 - x) (x - 2))/((x - 2) (x + 2)):
(2 (x - 2) (x + 2))/((x - 2) (x + 2)) + ((-x - 1) (x + 2))/((x - 2) (x + 2)) + ((4 - x) (x - 2))/((x - 2) (x + 2))

(2 (x - 2) (x + 2))/((x - 2) (x + 2)) + ((-x - 1) (x + 2))/((x - 2) (x + 2)) + ((4 - x) (x - 2))/((x - 2) (x + 2)) = (2 (x - 2) (x + 2) + (-x - 1) (x + 2) + (4 - x) (x - 2))/((x - 2) (x + 2)):


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

(x - 2) (x + 2) = (x) (x) + (x) (2) + (-2) (x) + (-2) (2) = x^2 + 2 x - 2 x - 4 = x^2 - 4:
(2 x^2 - 4 + (-x - 1) (x + 2) + (4 - x) (x - 2))/((x - 2) (x + 2))

2 (x^2 - 4) = 2 x^2 - 8:


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

(x + 2) (-x - 1) = (x) (-x) + (x) (-1) + (2) (-x) + (2) (-1) = -x^2 - x - 2 x - 2 = -x^2 - 3 x - 2:
(-8 + 2 x^2 + -x^2 - 3 x - 2 + (4 - x) (x - 2))/((x - 2) (x + 2))

(x - 2) (4 - x) = (x) (4) + (x) (-x) + (-2) (4) + (-2) (-x) = 4 x - x^2 - 8 + 2 x = -x^2 + 6 x - 8:
(-x^2 + 6 x - 8 + 2 x^2 - x^2 - 3 x - 8 - 2)/((x - 2) (x + 2))

 

Grouping like terms, 2 x^2 - x^2 - x^2 + 6 x - 3 x - 8 - 8 - 2 = (-3 x + 6 x) + (-8 - 2 - 8) + (2 x^2 - x^2 - x^2):
((-3 x + 6 x) + (-8 - 2 - 8) + (2 x^2 - x^2 - x^2))/((x - 2) (x + 2))

6 x - 3 x = 3 x:


(3 x + (-8 - 2 - 8) + (2 x^2 - x^2 - x^2))/((x - 2) (x + 2))

2 x^2 + (-x^2 - x^2) = 0:


(3 x + (-8 - 2 - 8))/((x - 2) (x + 2))

-8 - 2 - 8 = -18:


(3 x + -18)/((x - 2) (x + 2))

Factor 3 out of 3 x - 18:


(3 (x - 6))/((x - 2) (x + 2))=3x - 18 / x^2 - 4

a = 3      and     b=18

 Mar 31, 2019

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