Finding the transformation of a function of the form $f(x)=\\frac{mx+c}{x^2-d}$ to $f(ax)+b$.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "If $f(x)=\\simplify{({m}x+{c})/(x^2-{d})}$ for $x\\neq \\simplify{sqrt({d})}$, what is $\\simplify{f({a}x)+{b}}$?
", "advice": "To make the transformation from $f(x)=\\simplify{({m}x+{c})/(x^2-{d})}$ to $\\simplify{f({a}x)+{b}}$, we need to replace the $x$-terms in $f(x)$ with $\\simplify{{a}x}$ and then {aors} $\\var{abs(b)}$:
\n{advice}
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\"", "description": "", "templateType": "long string", "can_override": false}, "sol2": {"name": "sol2", "group": "Ungrouped variables", "definition": "\"\\\\[ \\\\begin{split} \\\\simplify{f({a}x)+{b}} &\\\\,= \\\\simplify[unitFactor,!expandBrackets]{({m}({a}x)+{c})/(({a}x)^2-{d})+{b}} \\\\\\\\ &\\\\,=\\\\simplify[unitFactor,!expandBrackets]{({m*a}x+{c})/({a^2}x^2-{d})+{b}}\\\\\\\\ &\\\\,=\\\\simplify[unitFactor,!expandBrackets]{({simp}({m*a/simp}x+{c/simp}))/({facden}({(a^2)/facden}x^2-{d/facden}))+{b}}. \\\\end{split} \\\\]
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