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