Question

Will medal and fan, equation in question

Answer 1

\[\frac{ 1 }{ x+4 }=\frac{ 1 }{ x ^{2}+3x-4 }+\frac{ 4 }{ x-1 }\]

Answer 2

Step 1: Factor
(hint: use the denominators of the other fractions as a suggestion for possible factors of the quadratic form)\[\frac{1}{x+4}=\frac{1}{(x+4)(x-1)}+\frac{4}{x-1}\]Step 2: Multiply the whole equation by (x+4)(x-1) to eliminate all the denominators
\[\frac{(x+4)(x-1)}{x+4}=\frac{(x+4)(x-1)}{(x+4)(x-1)}+\frac{4(x+4)(x-1)}{x-1}\]\[(x-1)=1+4(x+4)\]Step 3: Simplify
\[x=2+4x+16\]\[x=18+4x\]\[-3x=18\]Therefore: \[x=-6\]

Answer 3

Finally once you get an answer to an algebra problem you should ALWAYS check to make sure it satisfies the original problem. I.e. substitute x=-6 into the the very first equation and make sure you get something that makes sense like:
1=1
-(2/3)=-(2/3)
etc
If you get nonsense like
1=3
-5=5
Then something went wrong and you should recheck your calculation. Please note this is the single EASIEST way to make sure you got the right answer.

Answer 4

Thank you so much :3 this really helped out and i understand much better