Finding the transformation of a function of the form $f(x)=\\frac{mx+c}{x^2-d}$ to $af(x+b)$.
", "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 $\\simplify{{a}f(x+{b})}$?
", "advice": "To make the transformation from $f(x)=\\simplify{({m}x+{c})/(x^2-{d})}$ to $\\simplify{{a}f(x+{b})}$, we need to replace the $x$-terms in $f(x)$ with $\\simplify{x+{b}}$ and then multiply that function by $\\var{a}$:
\n{advice}
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\"", "description": "", "templateType": "long string", "can_override": false}, "sol2": {"name": "sol2", "group": "Ungrouped variables", "definition": "\"\\\\[ \\\\begin{split} \\\\simplify{{a}f(x+{b})} &\\\\,= \\\\var{a}\\\\left(\\\\simplify[unitFactor]{({m}(x+{b})+{c})/((x+{b})^2-{d})}\\\\right) \\\\\\\\ &\\\\,= \\\\var{a}\\\\left(\\\\simplify[unitFactor,!collectNumbers]{({m}x+{m*b}+{c})/((x^2+{2*b}x+{b^2})-{d})}\\\\right) \\\\\\\\&\\\\,= \\\\simplify[unitFactor]{{a}({m}x+{m*b+c})/(x^2+{2*b}x+{b^2-d})}\\\\\\\\&\\\\,= \\\\simplify[unitFactor]{{a*simp}({m/simp}x+{(m*b+c)/simp})/(x^2+{2*b}x+{b^2-d})}. \\\\end{split} \\\\]
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