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\((x+1)/(x-2)≥(x+3)/(x-4)\)

 Sep 1, 2020
 #1
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(x+1)/(x-2)≥(x+3)/(x-4)

 

Move the right to the left:


(x + 1) / (x - 2) - (x + 3) / (x - 4) >= 0

 

Find the LCD:

 

(x + 1)(x - 4) / (x - 2)(x - 4) - (x + 3)(x - 2) / (x - 4)(x - 2) >= 0

 

Combine the two fractions:

 

(x + 1)(x - 4) - (x + 3)(x - 2) / (x - 4)(x - 2) >= 0

 

Multiply both sides by (x - 4)(x - 2):

 

(x + 1)(x - 4) - (x + 3)(x - 2) >= 0

 

Expand:

 

x^2 - 3x - 4 - (x^2 + x - 6) >= 0

 

Distribute negative:

 

x^2 - 3x - 4 - x^2 - x + 6 >= 0

 

Combine like terms:

 

-4x + 2 >= 0

 

Subtract 2:


- 4x >= -2

 

Divide - 4:

 

x <= 1/2


:)
 

 Sep 1, 2020

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