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Mathematics

If x=5aba−bx = \dfrac{5ab}{a - b}, a ≠ b,

(a) Find : xa\dfrac{x}{a}

(b) Using properties of proportion, find: x+ax−a\dfrac{x + a}{x - a}

Ratio Proportion

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Answer

(a) Given,

x=5aba−bx = \dfrac{5ab}{a - b}

Multiplying 1a\dfrac{1}{a} on both sides of equation :

⇒xa=1a(5aba−b)⇒xa=5ba−b.\Rightarrow \dfrac{x}{a} = \dfrac{1}{a} \Big(\dfrac{5ab}{a - b}\Big) \\[1em] \Rightarrow \dfrac{x}{a} = \dfrac{5b}{a - b}.

Hence, xa=5ba−b.\dfrac{x}{a} = \dfrac{5b}{a - b}.

(b) Since,

xa=5ba−b\dfrac{x}{a} = \dfrac{5b}{a - b}

Applying componendo and dividendo, we get :

⇒x+ax−a=5b+(a−b)5b−(a−b)⇒x+ax−a=a+4b6b−a.\Rightarrow \dfrac{x + a}{x - a} = \dfrac{5b + (a - b)}{5b - (a - b)} \\[1em] \Rightarrow \dfrac{x + a}{x - a} = \dfrac{a + 4b}{6b - a}.

Hence, x+ax−a=a+4b6b−a.\dfrac{x + a}{x - a} = \dfrac{a + 4b}{6b - a}.

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