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 $f(\\simplify{{a}x+{b}})$?
", "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 $\\simplify{{a}x+{b}}$:
\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]{({m}({a}x+{b})+{c})/(({a}x+{b})^2-{d})} \\\\\\\\ &\\\\,= \\\\simplify[unitFactor,!collectNumbers]{({m*a}x+{m*b}+{c})/(({a^2}x^2+{2*a*b}x+{b^2})-{d})} \\\\\\\\ &\\\\,= \\\\simplify[unitFactor]{({m*a}x+{m*b+c})/({a^2}x^2+{2*a*b}x+{b^2-d})} \\\\\\\\ &\\\\,= \\\\simplify[unitFactor]{({m*a/simp}x+{(m*b+c)/simp})/({a^2/simp}x^2+{2*a*b/simp}x+{(b^2-d)/simp})}. \\\\end{split} \\\\]
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