Question

How do you solve `\frac { 4} { a } = \frac { 1} { a ^ { 2} + 4a } - \frac { a + 3} { a ^ { 2} + 4a }`?

Answer 1

Please see the explanation for a detailed description.

Explanation:

To avoid any solutions that would result in a division by 0 in the original equation, add the restrictions; `x !=0 and x !=-4`

`4/a = 1/(a^2+4a) - (a + 3)/(a^2+4a); x !=0 and x !=-4`

Now, it is ok to multiply both sides by by `a(a + 4)`:

`4(a + 4) = 1 - (a + 3); x !=0 and x !=-4`

Use the distributive property:

`4a + 16 = 1 - a - 3; x !=0 and x !=-4`

Combine like terms:

`5a = -18; x !=0 and x !=-4`

`a = -18/5`

The restrictions are dropped, because the solution is not one of them.