Question

Factorise 1/2a+b+2x=1/2a+1/b+1/2x

Answer 1

Answer:

- a and - b/2

Step-by-step explanation:

⇒ 1/( 2a + b + 2x ) = 1/2a + 1/b + 1/2x

⇒ 1/( 2a + b + 2x ) - 1/2x = 1/2a + 1/b

⇒ [ 2x - ( 2a + b + 2x ) ] / 2x( 2a + b + 2x ) = ( b + 2a ) / 2ab

⇒ [ 2x - 2a - b - 2x ] / 2x( 2a + b + 2x ) = ( b + 2a ) / 2ab

⇒ - ( 2a + b ) / 2x( 2a + b + 2x ) = ( b + 2a ) / 2ab

⇒ - 1  / 2x( 2a + b + 2x ) = 1 / 2ab

⇒ - 2ab = 2x( 2a + b + 2x )

⇒ - 2ab = 4ax + 2bx + 4x^2

⇒ 4x^2 + 2bx + 4ax + 2ab = 0

⇒ 4x^2 + 4ax + 2bx + 2ab = 0

⇒ 4x( x + a ) + 2b( x + a ) = 0

⇒ ( x + a )( 4x + 2b ) = 0

⇒ x = - a  or  x = - b/2