5sin²α+3cos²α / 3sin²α-5cos²α =

if tgα=√2

Tgα = tan (α) = sqrt (2) / 1 = opposite / adjacent

opposite = sqrt (2)

adjacent = 1

hypotenuse = sqrt (opposite^2 + adjacent^2)

= sqrt (sqrt (2) ^2 + 1^2) = sqrt (3)

sin (α) = opposite/hypotenuse

= sqrt (2) / sqrt (3)

cos (α) = adjacent/hypotenuse

= 1/sqrt (3)

now we can calculate the value of

5sin²α+3cos²α / 3sin²α-5cos²α

... do the math