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question: \dfrac{\left(\dfrac{a}{b}+11\right)}{\left(\dfrac{b}{a}−1-1\right)}

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Full solution

Q. question: \dfrac{\left(\dfrac{a}{b}+11\right)}{\left(\dfrac{b}{a}−1-1\right)}
  1. Simplify numerator: First, simplify the numerator ab+1\dfrac{a}{b} + 1.\newlineab+1=a+bb \dfrac{a}{b} + 1 = \dfrac{a + b}{b}
  2. Simplify denominator: Next, simplify the denominator ba−1\dfrac{b}{a} - 1.\newlineba−1=b−aa \dfrac{b}{a} - 1 = \dfrac{b - a}{a}
  3. Combine fractions: Now, we have the expression a+bbb−aa\dfrac{\dfrac{a + b}{b}}{\dfrac{b - a}{a}}.\newlinea+bbb−aa=a+bb×ab−a \dfrac{\dfrac{a + b}{b}}{\dfrac{b - a}{a}} = \dfrac{a + b}{b} \times \dfrac{a}{b - a}
  4. Multiply fractions: Multiply the fractions.\newline(a+b)⋅ab⋅(b−a)=a(a+b)b(b−a) \dfrac{(a + b) \cdot a}{b \cdot (b - a)} = \dfrac{a(a + b)}{b(b - a)}
  5. Simplify expression: Simplify the expression.\newlinea2+abb2−ab \dfrac{a^2 + ab}{b^2 - ab}

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