SOLUTION: Solve {{{4-(a-2)/(a+5)=(a^2-18)/(a+5)}}}

Question 125833: Solve

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Multiply both sides by the LCD . Doing this will eliminate every fraction.

Distribute and multiply. Notice every denominator has been canceled out.

Rearrange the terms

Distribute

Combine like terms

Subtract a^2 from both sides. Add 18 to both sides.

Combine like terms

Factor the left side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:
or

or Now solve for a in each case

So our possible answers are
or

However, if you plug in into the original equation , you'll get a denominator of zero. So is not a solution since is not in the domain.

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Answer:

So the only solution is

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