Question

Please help and show step by step pls

Answer 1

First notice that

x ² + 5x + 6 = (x + 3) (x + 2)

so you can rewrite everything with a common denominator:

5 / (x ² + 5x + 6) + 7 / (x + 2) = 6 / (x + 3)

5 / (x ² + 5x + 6) + 7 (x + 3) / ((x + 2) (x + 3)) = 6 (x + 2) / ((x + 3) (x + 2))

5 / (x ² + 5x + 6) + 7 (x + 3) / (x ² + 5x + 6) = 6 (x + 2) / (x ² + 5x + 6)

(5 + 7 (x + 3)) / (x ² + 5x + 6) = 6 (x + 2) / (x ² + 5x + 6)

As long as x ≠ -3 or x ≠ -2, the denominators are never zero, so we can cancel them and be left with

5 + 7 (x + 3) = 6 (x + 2)

Solving for x is easy from here:

5 + 7x + 21 = 6x + 12

7x - 6x = 12 - 5 - 21

x = -14