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