Answer:
[tex]a = 2[/tex] and [tex]b = 4[/tex]
Step-by-step explanation:
Given
The expression is:
[tex]\frac{x^2 + ax - 4}{x + 2} + \frac{x + b}{x + 2} = x + 1[/tex] --- missing from the question
Required
Find a and b
Take LCM
[tex]\frac{x^2 + ax - 4+x + b}{x + 2} = x + 1[/tex]
Cross Multiply
[tex]x^2 + ax - 4+x + b = (x+2)*(x + 1)[/tex]
Open brackets
[tex]x^2 + ax - 4+x + b = x^2+2x + x + 2[/tex]
[tex]x^2 + ax - 4+x + b = x^2+3x + 2[/tex]
Collect Like Terms
[tex]x^2 + ax +x + b- 4 = x^2+3x + 2[/tex]
[tex]x^2 + (a +1)x + b- 4 = x^2+3x + 2[/tex]
By comparing the coefficients:
[tex]a + 1 = 3[/tex]
[tex]a = 3 - 1[/tex]
[tex]a = 2[/tex]
[tex]b - 4 = 2[/tex]
[tex]b = 4[/tex]
Hence,
[tex]a = 2[/tex] and [tex]b = 4[/tex]
