SOLUTION: Hello, How do you solve: {{{ (x+3 )/ (x+5) + (6) / (x^2+3x-10) }}} Thanks

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hello, How do you solve: {{{ (x+3 )/ (x+5) + (6) / (x^2+3x-10) }}} Thanks      Log On


   

Question 731667: Hello, How do you solve:
+%28x%2B3+%29%2F+%28x%2B5%29+%2B+%286%29+%2F+%28x%5E2%2B3x-10%29+
Thanks
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2B3+%29%2F+%28x%2B5%29+%2B+6+%2F+%28x%5E2%2B3x-10%29.....factor %28x%5E2%2B3x-10%29...write 3x as 5x-2x

%28x%2B3+%29%2F+%28x%2B5%29+%2B+6+%2F+%28x%5E2%2B5x-2x-10%29...group

%28x%2B3+%29%2F+%28x%2B5%29+%2B+6+%2F+%28%28x%5E2%2B5x%29-%282x%2B10%29%29

%28x%2B3+%29%2F+%28x%2B5%29+%2B+6+%2F+%28x%28x%2B5%29-2%28x%2B5%29%29

%28x%2B3+%29%2F+%28x%2B5%29+%2B+6+%2F+%28%28x-2%29%28x%2B5%29%29....common denominator

%28%28%28x%2B3+%29%28x-2%29%29+%2B+6%29+%2F+%28%28x-2%29%28x%2B5%29%29

%28x%5E2-2x%2B3x-6+%2B+6%29+%2F+%28%28x-2%29%28x%2B5%29%29

%28x%5E2%2Bx%29+%2F+%28%28x-2%29%28x%2B5%29%29

x%28x%2B1%29+%2F+%28%28x-2%29%28x%2B5%29%29
since denominator cannot be equal to zero, we will find solutions if we set numerator equal to zero
x%28x%2B1%29=0
solutions:
x=0
and
x%2B1=0...=>...x=-1