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.
\[
h(x-1)=\frac{6}{5 x^{2}+22}
\]

Answer

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Answer

$\boxed{h(x-1)=\frac{6}{5(x-1)^{2}-3}}$

Steps

Step 1 ：The function $h$ is defined as $h(x)=\frac{6}{5 x^{2}-3}$.

Step 2 ：We are asked to find $h(x-1)$, which means we need to substitute $x-1$ into the function $h(x)$.

Step 3 ：Substituting $x-1$ into the function gives $h(x-1)=\frac{6}{5 (x-1)^{2}-3}$.

Step 4 ：Thus, the simplified expression for $h(x-1)$ is $h(x-1)=\frac{6}{5(x-1)^{2}-3}$.

Step 5 ：$\boxed{h(x-1)=\frac{6}{5(x-1)^{2}-3}}$