The function \( h \) is defined as \( h(x)=\frac{-6}{5 x^{2}+3} \). Find \( h(x-1) \). Write your answer without parentheses, and simplify it as much as possible.

To find \( h(x-1) \), we need to substitute \( x-1 \) into the function \( h \): \[ h(x-1) = \frac{-6}{5(x-1)^{2} + 3} \] Now we simplify \( (x-1)^{2} \): \[ (x-1)^{2} = x^{2} - 2x + 1 \] Now substitute this back into the equation: \[ h(x-1) = \frac{-6}{5(x^{2} - 2x + 1) + 3} \] Distributing the \( 5 \) gives: \[ h(x-1) = \frac{-6}{5x^{2} - 10x + 5 + 3} \] Now combine the constants: \[ h(x-1) = \frac{-6}{5x^{2} - 10x + 8} \] Thus, the simplified answer is: \[ \boxed{\frac{-6}{5x^{2} - 10x + 8}} \]