Answered

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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?

Sagot :

MrRoyal

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]

Det1Cass

Answer:

a = 2

b = 6

Edg 2021

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