SOLUTION: please help me with this problem. im getting confused. and i really need ur help. solve x-4 ---- x+1 + 4 -- x = 29 --- 30 {{{((x-4)/(x

Algebra ->  Test -> SOLUTION: please help me with this problem. im getting confused. and i really need ur help. solve x-4 ---- x+1 + 4 -- x = 29 --- 30 {{{((x-4)/(x      Log On


   

Question 173383: please help me with this problem. im getting confused. and i really need ur help.
solve
x-4
----
x+1

+
4
--
x
=
29
---
30

%28%28x-4%29%2F%28x%2B1%29%29%2B%284%2Fx%29=29%2F30
please show the work. thx!!

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28x-4%29%2F%28x%2B1%29%29%2B%284%2Fx%29=29%2F30

None of the denominators have any factors in common, so the lowest common denominator is simply the product of the three denominators, namely 30x%28x%2B1%29

Applying the LCD:



Now that you have the same denominator on both sides of the equation, you can multiply both sides by that same denominator and eliminate the denominator altogether, leaving only the numerators to deal with.

%2830x%28x-4%29%29%2B120%28x%2B1%29=29x%28x%2B1%29

Use the distributive property and then collect like terms:

30x%5E2-120x%2B120x%2B120=29x%5E2%2B29x

30x%5E2-29x%5E2-29x%2B120=0

x%5E2-29x%2B120=0

Since %28-5%29%28-24%29=120 and -5-24=-29, this quadratic equation factors:

x%5E2-29x%2B120=%28x-5%29%28x-24%29=0 so x=5 or x=24. However, since this is an equation involving rational expressions with variables in the denominator, you need to verify that you did not introduce extraneous roots in the process of solving. You can't have a root that makes any of the original denominators go to zero.

In this case, we are ok with both of the roots because neither of the roots of the quadratic cause any of the original denominators to be equal to zero. Furthermore, substitution of either of the roots into the original equation results in a true statement. You should do this verification work yourself to assure yourself that I didn't make a mistake somewhere.