Question

Sonya added two rational expressions, and then simplified her answer. The simplified answer was x + 1. What are the missing values in her original expression?

Answer 1

a = 2

b = 6

Edg 2021

Answer 2

`a = 2` and
`b = 4`

Explanation:

Given

The expression is:

`(x^2 + ax - 4)/(x + 2) + (x + b)/(x + 2) = x + 1` --- missing from the question

Required

Find a and b

Take LCM

`(x^2 + ax - 4+x + b)/(x + 2) = x + 1`

Cross Multiply

`x^2 + ax - 4+x + b = (x+2)*(x + 1)`

Open brackets

`x^2 + ax - 4+x + b = x^2+2x + x + 2`

`x^2 + ax - 4+x + b = x^2+3x + 2`

Collect Like Terms

`x^2 + ax +x + b- 4 = x^2+3x + 2`

`x^2 + (a +1)x + b- 4 = x^2+3x + 2`

By comparing the coefficients:

`a + 1 = 3`

`a = 3 - 1`

`a = 2`

`b - 4 = 2`

`b = 4`

Hence,

`a = 2` and
`b = 4`