{"version":"1.0","provider_name":"Rainbow Dash Network","provider_url":"http:\/\/rainbowdash.net\/","type":"link","title":"Gherkin \u2611\ufe0f (thelastgherkin)'s status on Friday, 08-Jun-12 18:53:09 UTC","author_name":"Gherkin \u2611\ufe0f (thelastgherkin)","author_url":"http:\/\/rainbowdash.net\/thelastgherkin","url":"http:\/\/rainbowdash.net\/notice\/1510101","html":"@<span class=\"vcard\"><a href=\"http:\/\/rainbowdash.net\/user\/131\" class=\"url\" title=\"Elliot\"><span class=\"fn nickname\">ecmc<\/span><\/a><\/span> Part c.  We divide f(x) by (x+2), which is a factor as we know from part a.  This gives us the expression (4x^2 - 8x +3).  So we whack that into the expression given in the question to get (2x^2 + x - 6) \/ (4x^2 - 8x +3)(x+2).  We can simplify it further than that!  (2x^2 + x - 6) can be simplified into (2x - 3)(x + 2).  (4x^2 - 8x + 3) can be simplified into (2x - 3)(2x -1).  The expression becomes (2x - 3)(x + 2) \/ (2x - 3)(x + 2)(x + 2).  We do this: (\u03362\u0336x\u0336 \u0336-\u0336 \u03363\u0336)\u0336(\u0336x\u0336 \u0336+\u0336 \u03362\u0336)\u0336 \/ (\u03362\u0336x\u0336 \u0336-\u0336 \u03363\u0336)\u0336(\u0336x\u0336 \u0336+\u0336 \u03362\u0336)\u0336(x + 2), giving us a final answer of 1\/(x + 2)."}