Question

What two rational expressions sum to
`(4x+2)/(x^(2)-9+8 )` Enter your answer by filling in the boxes. Enter your answer so that each rational expression is in simplified form.

Answer 1

Answer:4x+2/x2−9x+8 = −6/7(x−1) + 34/7(x−8)

Answer 2

`(4x+2)/(x^2 - 9x + 8) = (4x)/((x-8)(x-1)) + (2)/((x-8)(x-1))`

Explanation:

Given

`(4x+2)/(x^(2)-9+8 ) = (A)/(()(x-1)) + (B)/(()(x-8))`

Required

Fill in the gaps

Going by the given parameters, we have that

`(4x+2)/(x^(2)-9+8 ) = (A)/(()(x-1)) + (B)/(()(x-8))`

`x^2 - 9x + 8`, when factorized is
`(x-1)(x-8)`

Hence; the expression becomes

`(4x+2)/((x-1)(x-8)) = (A)/((x-8)(x-1)) + (B)/((x-1)(x-8))`

Combine Fractions

`(4x+2)/((x-1)(x-8)) = (A + B)/((x-8)(x-1))`

Simplify the denominators

`4x + 2 = A + B`

By direct comparison

`A = 4x`

`B = 2`

Hence, the complete expression is

`(4x+2)/(x^2 - 9x + 8) = (4x)/((x-8)(x-1)) + (2)/((x-8)(x-1))`