How do I solve a partial fractions question when $x$ can’t equal any solutions?

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How do I solve $A(i)$ and $A(ii)$ when $x$ can't equal $-2/5$ or $1/2$? The only method I’m aware of for partial fractions requires these values to be subbed in and I’m confused. Sorry if the image is obstructed by my scruffy writing. If it’s helpful, part $b$ involves binomial expansion.