What is true about the solution of x 2^

/2x-6=9/6x-18

solution of the equation are x = 3 and x = ±√3

Step-by-step explanation:

Given in the question an equation

x² / (2x-6) = 9 / (6x-18)

Step1

cross multiplication

x² (6x - 18) = 9 (2x - 6)

Step2

apply distributive law

6x³ - 18x² = 18x - 54

step3

rearrange the terms

6x³ - 18x² - 18x + 54 = 0

step4

divide by 6

x³ - 3x² - 3x + 9 = 0

x² (x-3) - 3 (x-3) = 0

(x-3) (x²-3) = 0

Step5

x = 3 and x² = 3

for factor x² = 3

take square root on both sides

√x² = √3

x = ±√3