Question

Solve each of the following quadratic equation: ,


$\frac{a}{(ax - 1)} + \frac{b}{(bx - 1)} = (a + b) , \:$
x # 1 / a , 1 / b.


Quadratic Equations

Class 10

Answer 1

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

$=>[\frac{a}{ax - 1} - b]+[\frac{b}{bx - 1} - a] = 0$

$=>[\frac{a -b(ax - 1)}{ax - 1}]+[\frac{b - a(bx - 1)}{bx - 1}] = 0$

$=>[\frac{a - abx + b}{ax - 1}+\frac{a - abx + b}{bx - 1}] = 0$

$=>(a - abx + b)[\frac{1}{ax - 1}+\frac{1}{bx - 1}] = 0$

$=>(a - abx + b)[\frac{bx - 1 + ax - 1}{(ax - 1)(bx - 1)}] = 0$

$=>(a - abx + b)[\frac{bx + ax - 2}{(ax-  1)(bx - 1)}] = 0$

$=>(a - abx + b)[\frac{(b + a)x - 2}{(ax - 1)(bx - 1)}] = 0$

$=>(a - abx + b)[(b + a)x - 2] = 0$

(i)

⇒ a - abx + b = 0

⇒ a + b = abx

⇒ x = (a + b)/ab

(ii)

⇒ (b + a)x - 2 = 0

⇒ (b + a)x = 2

⇒ x = (2/a + b).

Therefore, x = (a + b)/ab (or) x = 2/a + b.

Hope this helps!

Answer 2

HEY THERE!!

Conclusion;-

Therefore, x = (a + b)/ab

x = 2/a + b.