[tex]y = \sqrt{ \frac{5x+3}{x-5} } [/tex]
[tex] y^{2} = \frac{5x+3}{x-5} [/tex]
Transpose the equation to eliminate any fractions:
[tex] y^{2}(x-5) = 5x+3 [/tex]
Expand the brackets:
[tex]x y^{2} - 5 y^{2} = 5x+3 [/tex]
Put x terms on one side and the others on the other side:
[tex] xy^{2} - 5x = 5y^{2}+3 [/tex]
Factorise to take x out of the terms:
[tex]x(y^{2} - 5) = 5 y^{2} +3[/tex]
Transpose to leave only x on the left hand side of the equation:
∴[tex]x = \frac{5 y^{2} + 3 }{ y^{2} -5 } [/tex]
