Question

Solve the equation. A/a+3=2a/a-3-1

Answer 1

hello here is a solution : 

Answer 2

a = -1

and a ≠ -3 , 3

Explanation:

Given Equation :

`(a)/(a+3)=(2a)/(a-3)-1`

We need to solve the given equation.

Clearly given equation has 2 rational terms.

We know that Denominator of rational Numbers can not be equal to 0.

So, a + 3 ≠ 0 ⇒ a ≠ - 3 and a - 3 ≠ 0 ⇒ a ≠ + 3

⇒ a can not be equal to 3 and -3.

Now Consider,

`(a)/(a+3)=(2a)/(a-3)-1`

`(a)/(a+3)=(2a-(a-3))/(a-3)`

`(a)/(a+3)=(2a-a+3)/(a-3)`

`(a)/(a+3)=(a+3)/(a-3)`

`a(a-3)=(a+3)(a+3)`

`a^2-3a=a^2+2(a)(3)+(3)^2`

`a^2-3a=a^2+6a+9`

`6a+3a=-9`

`9a=-9`

`a=-1`

Therefore, a = -1