Chose the similarity criteria that proves the two triangles to be similar

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mine9226

11.08.2022

Mathematics

$y = \sqrt{ \frac{5x+3}{x-5} }$
$y^{2} = \frac{5x+3}{x-5}$
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:
∴ $x = \frac{5 y^{2} + 3 }{ y^{2} -5 }$

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