Question

9. 10. To solve 2x x 2 11 x = 8 x 2 2x , Ren multiplied both sides by the least common denominator. Which statement is true? A. 2 is an extraneous solution. B. 7 2 is an extraneous solution. C. 0 and 2 are extraneous solutions. D. This equation does not contain any extraneou

Answer 1

2 is the extraneous solution

Explanation:

Given equation is

`(2x)/(x-2) -(11)/(x) =(8)/(x^2-2x)`

Factor the denominator

`(2x)/(x-2) -(11)/(x) =(8)/(x(x-2))`

LCD is x(x-2), multiply all the fractions by LCD

`2x \cdot x-11(x-2)=8`

`2x^2-11x+22= 8`, subtract 8 from both sides

`2x^2-11x+14=0`

factor the left hand side

`2x^2-7x-4x+14= 0`

`x(2x-7)-2(2x-7)=0`

`(x-2)(2x-7)=0`

x-2=0, so x=2

2x-7=0,
`x=(7)/(2)`

when x=2, then the denominator becomes 0 that is undefined

So 2 is the extraneous solution