Question

HELP
list all the extraneous solutions of the equation 2x/x+4 = x/x-1

Answer 1

Explanation:

2x x(x-1) = x x (x+4)

2x x (x-1) - x x (x+4)= 0

2x^2 - 2x - x x (x+4) = 0

2x^2 - 2x - x^2 - 4x = 0

x^2 - 2x - 4x = 0

x^2 - 6x = 0

x x (x-6) = 0

x = 0

x - 6 = 0

x = 6

The equation has 2 solutions

x1 = 0, x2 = 6

Answer 2

`\huge\boxed{\sf Solution\ Set = \{0,6\}}`

Explanation:

`\displaystyle (2x)/(x+4) = (x)/(x-1) \\\\Cross \ Multiplying \\\\x(x+4) = 2x(x-1)\\\\x^2 + 4x = 2x^2 -2x\\\\2x^2 -x^2 = 4x + 2x\\\\x^2 = 6x \\\\x^2 -6x = 0\\\\Either,\\\\x = 0 \ \ \ \ OR \ \ \ \ x-6 = 0\\\\x = 0 \ \ \ \ OR \ \ \ \ x = 6`

Hence,

Solution Set = {0,6}

`\rule[225]{225}{2}`

Hope this helped!

~AH1807