Question

Solve for x: 2 over quantity x minus 2 plus 7 over quantity x squared minus 4 equals 5 over x.

x = negative 4 over 3 and x = –5

x = negative 4 over 3 and x = 5

x = 4 over 3 and x = –5

x = 4 over 3 and x = 5

Answer 1

The first choice

Explanation:

Answer 2

Answer: The correct option is

(B)
`x=-(4)/(3),~~5.`

Step-by-step explanation: We are given to solve the following equation for x :

"2 over quantity x minus 2 plus 7 over quantity x squared minus 4 equals 5 over x."

The above equation can be written as :

`(2)/(x-2)+(7)/(x^2-4)=(5)/(x)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

We will be using the following formula to solve equation (i) :

`a^2-b^2=(a+b)(a-b).`

The solution of equation (i) is as follows :

`(2)/(x-2)+(7)/(x^2-4)=(5)/(x)\\\\\\\Rightarrow (2)/(x-2)+(7)/((x+2)(x-2))=(5)/(x)\\\\\\\Rightarrow (2(x+2)+7)/((x+2)(x-2))=(5)/(x)\\\\\\\Rightarrow (2x+11)/(x^2-4)=(5)/(x)\\\\\Rightarrow 2x^2+11x=5x^2-20\\\\\Rightarrow 5x^2-2x^2-11x-20=0\\\\\Rightarrow 3x^2-11x-20=0\\\\\Rightarrow 3x^2-15x+4x-20=0\\\\\Rightarrow 3x(x-5)+4(x-5)=0\\\\\Rightarrow (3x+4)(x-5)=0\\\\\Rightarrow 3x+4=0,~~~x-5=0\\\\\Rightarrow x=-(4)/(3),~5.`

Thus, the required solution of the given equation is

`x=-(4)/(3),~~5.`

Option (B) is CORRECT.