Step 1 :Add 7 to both sides: \(g + 7 = \frac{c + 3}{4 + c}\)
Step 2 :Multiply both sides by \((4 + c)\): \((g + 7)(4 + c) = c + 3\)
Step 3 :Expand and simplify: \(4g + gc + 28 + 7c = c + 3\)
Step 4 :Rearrange to solve for c: \(gc + 6c - 4g = -25\)
Step 5 :Factor out c: \(c(g + 6) = 4g - 25\)
Step 6 :Divide by \((g + 6)\): \(c = \frac{4g - 25}{g + 6}\)
Step 7 :\(\boxed{c = \frac{4g - 25}{g + 6}}\)