Question

Plato!! Please help!!!

Answer 1

`a =7`
`b = 2`
`c = -4`

Explanation:

Given

`(3x)/(x + 2) + (4x)/(x - 2) = (ax^2 + bx)/(x^2 + c)`

Required

Find a, b and c

`(3x)/(x + 2) + (4x)/(x - 2) = (ax^2 + bx)/(x^2 + c)`

Take LCM

`(3x(x -2) + 4x(x+2))/((x + 2)(x - 2)) = (ax^2 + bx)/(x^2 + c)`

Expand

`(3x^2 -6x + 4x^2+8x)/(x^2 - 4) = (ax^2 + bx)/(x^2 + c)`

Collect like terms

`(3x^2 + 4x^2-6x+8x)/(x^2 - 4) = (ax^2 + bx)/(x^2 + c)`

`(7x^2+2x)/(x^2 - 4) = (ax^2 + bx)/(x^2 + c)`

By direct comparison:

`ax^2= 7x^2 \to a = 7`

`bx = 2x \to b = 2`

`-4 = c \to c = -4`