Question

1. solve, state non-permissible values: \\(\frac{4}{q + 8} = \frac{3}{q + 5}\\)

Explanation:

Step1: Find non-permissible values

Set denominators to 0:
$q+8=0 \implies q=-8$
$q+5=0 \implies q=-5$

Step2: Cross-multiply to eliminate fractions

$4(q+5) = 3(q+8)$

Step3: Expand both sides

$4q + 20 = 3q + 24$

Step4: Isolate variable $q$

$4q - 3q = 24 - 20$
$q = 4$

Step5: Verify solution validity

$q=4$ is not $-8$ or $-5$, so it is valid.

Answer:

Non-permissible values: $q=-8$ and $q=-5$
Solution: $q=4$