Answer:
x = [tex]\frac{1+4y^2}{y^2-1}[/tex]
Step-by-step explanation:
Given
y = [tex]\sqrt{\frac{x+1}{x-4} }[/tex] ( square both sides to clear the radical )
y² = [tex]\frac{x+1}{x-4}[/tex] ( multiply both sides by (x - 4) )
y²(x - 4) = x + 1 ← distribute parenthesis on left side )
xy² - 4y² = x + 1 ( add 4y² to both sides )
xy² = x + 1 + 4y² ( subtract x from both sides )
xy² - x = 1 + 4y² ( factor out x from each term on the left side )
x(y² - 1) = 1 + 4y² ← divide both sides by (y² - 1)
x = [tex]\frac{1+4y^2}{y^2-1}[/tex]
