Question

Question Number : 12
Please Full Solution.

Answer 1

Answer :

Now,

1/(a + b + x) = 1/a + 1/b + 1/x

⇒ 1/(a + b + x) - 1/x = 1/a + 1/b

⇒ {x - (a + b + x)}/{x (a + b + x) = (b + a)/ab

⇒ (x - a - b - x)/{x (a + b + x)} = (b + a)/ab

⇒ (- a - b)/{x (a + b + x)} = (a + b)/ab

⇒ - (a + b)/{x (a + b + x)} = (a + b)/ab

⇒ - 1/{x (a + b + x)} = 1/ab, cancelling (a + b) from both sides

⇒ x (a + b + x) = - ab, by cross multiplication

⇒ x (a + b + x) + ab = 0

⇒ ax + bx + x² + ab = 0

⇒ x² + ax + bx + ab = 0,

which is the required simplified form of the given equation.

[Note : Here, both (ab) and (a + b) are non-zero]

Further, we proceed to solve the equation.

Now, x² + ax + bx + ab = 0

⇒ x (x + a) + b (x + a) = 0

⇒ (x + a) (x + b) = 0

∴ either x + a = 0 or, x + b = 0

⇒ x = - a, - b

∴ the required solution of the given equation be

x = - a, - b

Hope it helps!

Answer 2

$\bold {\huge{Ello!!}}$

$<b >Here's your answer$

_______________________

• Simplifying the following equation :

1 / ( a + b + x ) = 1 / a + 1 / b + 1 / x

=> 1 / ( a + b + x ) - 1 / x = 1 / a + 1 / b

=> ( x - a - b - x ) / x ( a + b + x ) = ( b + a ) / ab

=> - ( a + b ) / x ( a + b + x ) = ( a + b ) / ab

=> - 1 / ax + bx + x² = 1 / ab

=> ax + bx + x² = - ab

=> ax + bx + x² + ab = 0

=> ax + ab + x² + bx = 0

=> a ( x + b ) + x ( x + b ) = 0

=> ( x + b ) + ( a + x ) = 0

Now ,

•°• either , ( x + b ) = 0 or , ( a + x ) = 0

x = - b x = - a

So , x = - a , - b [ ★ Required answer ]

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$<b><u><marquee direction> Hope it helps !!$