Question

Simplify. State the result in simplest form.

Answer 1

`\cfrac{2x+10}{x^2+x-2}+\cfrac{2}{x+2}+\cfrac{x}{x-1}\implies \cfrac{2x+10}{(x-1)(x+2)}+\cfrac{2}{x+2}+\cfrac{x}{x-1} \\\\\\ \cfrac{(1)(2x+10)~~ + ~~(x-1)(2)~~ + ~~(x+2)(x)}{\underset{\textit{using this as our LCD}}{(x-1)(x+2)}} \\\\\\ \cfrac{2x+10~~ + ~~2x-2~~ + ~~x^2+2x}{(x-1)(x+2)}\implies \cfrac{x^2+6x+8}{(x-1)(x+2)} \\\\\\ \cfrac{(x+2)(x+4)}{(x-1)(x+2)}\implies \cfrac{x+4}{x-1}`

Answer 2

1st option

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