Question

Solving Rational equations. LCD method. Show work.


`(2a-3)/(a-3) -2= (12)/(a+3)`

Answer 1

a = 5

Explanation:

LCD: ( a+b)(a-b)

so

(2a-3)(a+3) - 2(a+3)(a-3) = 12(a-3)

2a^2 + 6a - 3a - 9 -2a^2 + 18 = 12a - 36

3a + 9 = 12a - 36

3a - 12a = -36 - 9

-9a = -45

a = 5

-

Answer 2

a = 5 is the answer.

Explanation:

We have given rational equation.

We have to solve this rational equation.

For this, we first find the LCM of the rational equation.

That is (a-3)(a+3) .

Multiply this LCM to each term of the rational equation we get,

(2a-3)(a+3) - 2(a-3)(a+3) =12(a-3)

2a²+6a-3a-9-2(a²+3a-3a-9) = 12a-36

2a²+6a-3a-9-2a²+18 = 12a -36

3a +9 = 12a - 36

12a -3a = 9+36

9a =45

a = 5

a = 5 is the solution of the given rational equation.