Question

a/ax + 1 - b/bx +1 = a - b

Answer 1

Solution :

$Now,\:\frac{a}{ax+1}-\frac{b}{bx+1}=a-b$

$\implies \frac{a(bx+1)-b(ax+1)}{(ax+1)(bx+1)}=a-b$

$\implies \frac{abx+a-abx-b}{abx^{2}+(a+b)x+1}=a-b$

$\implies \frac{a-b}{abx^{2}+(a+b)x+1}=a-b$

{ Dividing both sides by (a - b) }

$\implies abx^{2}+(a+b)x+1=1$

{ Subtracting 1 from both sides }

$\implies abx^{2}+(a+b)x=0$

$\implies x \{abx+(a+b)\}=0$

Either, x = 0 or, abx + (a + b) = 0

⇒ x = 0, x = $-\frac{a+b}{ab}$ ,

which is the required solution.