Question

a/x-b+b/x-a=2,find x

Answer 1

Question :-

$\sf \: if \: \frac{a}{x - b} + \frac{b}{x - a} = 2 \: \: then \: find \: x \:$

Answer :-

Solution :-

We have ,

$\to \sf\frac{a}{x - b} + \frac{b}{x - a} = 2 \: \: \\ \\ \to \: \sf \frac{a(x - a) + b(x - b)}{(x - a)(x - b)} = 2 \\ \\ \to \sf \frac{ax - {a}^{2} + bx - {b}^{2} }{ {x}^{2} - bx - ax + ab } = 2 \\ \\ \to \sf ax + bx - {a}^{2} - {b}^{2} = 2 {x}^{2} - 2bx - 2ax + 2ab \\ \\ \to \sf \: 2 {x}^{2} - 3bx - 3ax + {a}^{2} + {b}^{2} + 2ab \\ \\ \to \sf 2 {x}^{2} - 3bx - 3ax + {(a + b)}^{2}$

Answer 2

Question :-

\begin{lgathered}\sf \: if \: \frac{a}{x - b} + \frac{b}{x - a} = 2 \: \: then \: find \: x \: \\\end{lgathered}

if

x−b

a

+

x−a

b

=2thenfindx

Answer :-

Solution :-

We have ,

\begin{lgathered}\to \sf\frac{a}{x - b} + \frac{b}{x - a} = 2 \: \: \\ \\ \to \: \sf \frac{a(x - a) + b(x - b)}{(x - a)(x - b)} = 2 \\ \\ \to \sf \frac{ax - {a}^{2} + bx - {b}^{2} }{ {x}^{2} - bx - ax + ab } = 2 \\ \\ \to \sf ax + bx - {a}^{2} - {b}^{2} = 2 {x}^{2} - 2bx - 2ax + 2ab \\ \\ \to \sf \: 2 {x}^{2} - 3bx - 3ax + {a}^{2} + {b}^{2} + 2ab \\ \\ \to \sf 2 {x}^{2} - 3bx - 3ax + {(a + b)}^{2}\end{lgathered}

→

x−b

a

+

x−a

b

=2

→

(x−a)(x−b)

a(x−a)+b(x−b)

=2

→

x

2

−bx−ax+ab

ax−a

2

+bx−b

2

=2

→ax+bx−a

2

−b

2

=2x

2

−2bx−2ax+2ab

→2x

2

−3bx−3ax+a

2

+b

2

+2ab

→2x

2

−3bx−3ax+(a+b)

2