SOLUTION: 9. (8 pts) Solve the equation. Check all proposed solutions. Show work in solving and in checking, and state your final conclusion. (x-3)/(x+2)-10/(x^2+2x)=0  

Algebra ->  Equations -> SOLUTION: 9. (8 pts) Solve the equation. Check all proposed solutions. Show work in solving and in checking, and state your final conclusion. (x-3)/(x+2)-10/(x^2+2x)=0         Log On


   

Question 1134678: 9. (8 pts) Solve the equation. Check all proposed solutions. Show work in solving and in checking, and state your final conclusion.

(x-3)/(x+2)-10/(x^2+2x)=0
 
Found 2 solutions by mathsolverplus, MathLover1:
Answer by mathsolverplus(88) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-3%29%2F%28x%2B2%29-10%2F%28x%5E2%2B2x%29=0+
x%28x-3%29-10%29=0 Multiplied x%5E2%2B2x on both sides.
x%5E2-3x-10=0
%28x-5%29%28x%2B2%29=0
x=-2 and x=5
x cannot be -2 because we have (x+2) as the denominator.
Otherwise, you will obtain error from the first part: (x-3)/(0)





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Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-3%29%2F%28x%2B2%29-10%2F%28x%5E2%2B2x%29=0+

%28x-3%29%2F%28x%2B2%29-10%2Fx%28x%2B2%29=0+ ..........common denominator is x%28x%2B2%29

x%28x-3%29%2Fx%28x%2B2%29-10%2Fx%28x%2B2%29=0+

%28x%28x-3%29-10%29%2Fx%28x%2B2%29=0+

%28x%5E2-3x-10%29%2Fx%28x%2B2%29=0+ ...factor numerator

%28%28x+%2B+2%29+%28x+-+5%29%29%2Fx%28x%2B2%29=0+.....since numerator and denominator have x%2B2=0=> x=-2 is not a solution because denominator cannot be equal to zero
%28cross%28%28x+%2B+2%29%29+%28x+-+5%29%29%2Fxcross%28%28x%2B2%29%29=0+......simplify

+%28x+-+5%29%2Fx=0+

since denominator cannot be equal to zero (function would be undefined), exclude value x=0
solution is:

+x+-+5=0+=>x=5