{
  "unit": 4,
  "title": "Rational Expressions, Equations & Functions",
  "terms": [
    {
      "en": "rational expression",
      "es": "expresión racional",
      "fr": "expression rationnelle",
      "ar": "تعبير نسبي",
      "pt": "expressão racional",
      "definition": "A quotient of two polynomials with a nonzero denominator."
    },
    {
      "en": "domain restriction",
      "es": "restricción del dominio",
      "fr": "restriction du domaine",
      "ar": "قيد المجال",
      "pt": "restrição de domínio",
      "definition": "An input excluded because it makes a denominator zero."
    },
    {
      "en": "equivalent rational expressions",
      "es": "expresiones racionales equivalentes",
      "fr": "expressions rationnelles équivalentes",
      "ar": "تعبيرات نسبية متكافئة",
      "pt": "expressões racionais equivalentes",
      "definition": "Quotients equal throughout their shared allowed domain."
    },
    {
      "en": "multiplication of rational expressions",
      "es": "multiplicación de expresiones racionales",
      "fr": "multiplication d'expressions rationnelles",
      "ar": "ضرب التعابير النسبية",
      "pt": "multiplicação de expressões racionais",
      "definition": "Multiply numerators and denominators, then simplify without losing restrictions."
    },
    {
      "en": "division of rational expressions",
      "es": "división de expresiones racionales",
      "fr": "division d'expressions rationnelles",
      "ar": "قسمة التعابير النسبية",
      "pt": "divisão de expressões racionais",
      "definition": "Multiply by the reciprocal of a nonzero divisor."
    },
    {
      "en": "least common denominator",
      "es": "mínimo común denominador",
      "fr": "plus petit dénominateur commun",
      "ar": "المقام المشترك الأصغر",
      "pt": "mínimo denominador comum",
      "definition": "A common denominator divisible by each original denominator."
    },
    {
      "en": "addition of rational expressions",
      "es": "suma de expresiones racionales",
      "fr": "addition d'expressions rationnelles",
      "ar": "جمع التعابير النسبية",
      "pt": "adição de expressões racionais",
      "definition": "Rewrite with a common denominator before adding numerators."
    },
    {
      "en": "subtraction of rational expressions",
      "es": "resta de expresiones racionales",
      "fr": "soustraction d'expressions rationnelles",
      "ar": "طرح التعابير النسبية",
      "pt": "subtração de expressões racionais",
      "definition": "Rewrite with a common denominator before subtracting numerators."
    },
    {
      "en": "rational equation",
      "es": "ecuación racional",
      "fr": "équation rationnelle",
      "ar": "معادلة نسبية",
      "pt": "equação racional",
      "definition": "An equation containing rational expressions and excluded denominator values."
    },
    {
      "en": "extraneous solution",
      "es": "solución extraña",
      "fr": "solution extrinsèque",
      "ar": "حل دخيل",
      "pt": "solução extrínseca",
      "definition": "A candidate root produced during algebraic steps that fails the original equation."
    },
    {
      "en": "reciprocal function",
      "es": "función recíproca",
      "fr": "fonction inverse multiplicative",
      "ar": "دالة المقلوب",
      "pt": "função recíproca",
      "definition": "A function such as f(x)=1/x, undefined where its denominator is zero."
    },
    {
      "en": "vertical asymptote",
      "es": "asíntota vertical",
      "fr": "asymptote verticale",
      "ar": "خط تقارب رأسي",
      "pt": "assíntota vertical",
      "definition": "A vertical line approached by function values becoming unbounded."
    },
    {
      "en": "horizontal asymptote",
      "es": "asíntota horizontal",
      "fr": "asymptote horizontale",
      "ar": "خط تقارب أفقي",
      "pt": "assíntota horizontal",
      "definition": "A line y=L approached as x tends to positive or negative infinity."
    },
    {
      "en": "removable discontinuity",
      "es": "discontinuidad removible",
      "fr": "discontinuité amovible",
      "ar": "انقطاع قابل للإزالة",
      "pt": "descontinuidade removível",
      "definition": "A missing point where a finite two-sided limit exists."
    },
    {
      "en": "rational transformation",
      "es": "transformación racional",
      "fr": "transformation rationnelle",
      "ar": "تحويل الدالة النسبية",
      "pt": "transformação racional",
      "definition": "A shift, reflection, or scale of a rational parent function."
    },
    {
      "en": "direct variation",
      "es": "variación directa",
      "fr": "proportionnalité directe",
      "ar": "تناسب طردي",
      "pt": "variação direta",
      "definition": "A relation y=kx with constant k."
    },
    {
      "en": "inverse variation",
      "es": "variación inversa",
      "fr": "proportionnalité inverse",
      "ar": "تناسب عكسي",
      "pt": "variação inversa",
      "definition": "A relation y=k/x for nonzero x and constant k."
    },
    {
      "en": "joint variation",
      "es": "variación conjunta",
      "fr": "variation conjointe",
      "ar": "تناسب مشترك",
      "pt": "variação conjunta",
      "definition": "A relation such as z=kxy involving multiple factors."
    },
    {
      "en": "rational rate model",
      "es": "modelo racional de tasas",
      "fr": "modèle rationnel de taux",
      "ar": "نموذج نسبي للمعدلات",
      "pt": "modelo racional de taxas",
      "definition": "A quotient-based model of work rates, speeds, or related quantities."
    }
  ],
  "schema_version": "1.1"
}