Question

Can someone solve for x please:

Answer 1

Of course you could solve for x.  The LCD of these three fracgtions is (x-2)(x+2)(x).

However, you could identify the correct answer by subbing the given x values into the original equation of fractions.  For example, if you want to test out x = -4/3 and x = -5, focus on one or the other first.  If x = -4/3

then the first fraction becomes

     2
-------------     Calculate the other 2 fractions for x = -4/3.  Is the resulting 
-4/3 - 6/3      equation then true?

Answer 2

THe LCD is x(x^2 - 4)

so multiplying through by this we get:-

2x(x + 2) + 7x =  5(x^2 - 4)
2x^2 + 4x + 7x = 5x^2 - 20
3x^2 - 11x  - 20 = 0

(3x + 4)(x - 5 ) =  0

so x =  5 , -4/3

Its the second choice