Question

Solve for x: 1/a+1/b+1/x=1/a+b+x​

Answer 1

Answer:

- a , - b.

Step-by-step explanation:

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

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

⇒ ( a + b ) / ab = [ x - ( a + b + x ) ] / x( a + b + x )

⇒ ( a + b ) / ab = [ x - a - b - x ] / x( a + b + x )

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

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

⇒ 1 / ab = - 1 / x( a + b + x )

⇒ x( a + b + x ) = - ab

⇒ ax + xb + x^2 = - ab

⇒ x^2 + xb + ax + ab = 0

⇒ x( x + b ) + a( x + b ) = 0

⇒ ( x + a )( x + b ) = 0

Using zero product rule, either x + a = 0 or x + b = 0

So, either x = - a  or x = - b

Answer 2

plz refer to this attachment