(5x-4)/(2x-8)=(20)/((x+4)(x-4))

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Solution for (5x-4)/(2x-8)=(20)/((x+4)(x-4)) equation: 



(5x-4)/(2x-8)=(20)/((x+4)(x-4))

We move all terms to the left:

(5x-4)/(2x-8)-((20)/((x+4)(x-4)))=0



Domain of the equation: (2x-8)!=0

We move all terms containing x to the left, all other terms to the right

2x!=8

x!=8/2

x!=4

x∈R





Domain of the equation: ((x+4)(x-4)))!=0

x∈R



We use the square of the difference formula

x^2+(5x-4)/(2x-8)+16=0

We multiply all the terms by the denominator


x^2*(2x-8)+(5x-4)+16*(2x-8)=0

We multiply parentheses

x^2*(2x-8)+(5x-4)+32x-128=0

We get rid of parentheses

x^2*(2x-8)+5x+32x-4-128=0

We add all the numbers together, and all the variables

x^2*(2x-8)+37x-132=0

We move all terms containing x to the left, all other terms to the right

x^2*(2x-8)+37x=132

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