Solve the equation. Check the solution.

g plus four over g minus two equals g minus five over g minus eight

1 answer

To solve the equation (g + 4)/(g - 2) = (g - 5)/(g - 8), we first need to cross multiply to get rid of the fractions:

(g + 4)(g - 8) = (g - 5)(g - 2)
Expanding both sides:

g^2 - 8g + 4g - 32 = g^2 - 2g - 5g + 10
g^2 - 4g - 32 = g^2 - 7g + 10
Subtracting g^2 from both sides:

-4g - 32 = -7g + 10
Adding 7g to both sides:

3g - 32 = 10
Adding 32 to both sides:

3g = 42
Dividing by 3:

g = 14

To check our solution, we substitute g = 14 back into the original equation:

(14 + 4)/(14 - 2) = (14 - 5)/(14 - 8)
18/12 = 9/6
3/2 = 3/2

The solution checks out, so g = 14 is the correct solution.