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

Answer:

a = 2

b = 6

Edg 2021

Answer 2

Answer:

$a = 2$ and $b = 4$

Step-by-step explanation:

Given

The expression is:

$\frac{x^2 + ax - 4}{x + 2} + \frac{x + b}{x + 2} = x + 1$ --- missing from the question

Required

Find a and b

Take LCM

$\frac{x^2 + ax - 4+x + b}{x + 2} = x + 1$

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 $b = 4$