Question

Solve (x+5)/(x+8)=1+(6)/(x+1)

Answer 1

x = -5 2/3

Explanation:

You want the solution to the rational equation ...

(x+5)/(x+8)=1+(6)/(x+1)

F(x) = 0

Casting this into the form f(x) = 0, we have ...

`(x+5)/(x+8)=1+(6)/(x+1)\\\\\\1-(3)/(x+8)=1+(6)/(x+1)\\\\\\(6)/(x+1)+(3)/(x+8)=0\\\\\\(3(2(x+8)+(x+1)))/((x+1)(x+8))=0\\\\\\3x+17=0\qquad\text{the numerator is zero when the fraction is zero}\\\\\\\boxed{x=-(17)/(3)}`

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Additional comment

The attachment shows the left side and right side expressions are equal when x = -17/3 = -5 2/3.

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