SOLUTION: Can you help me solve and show solution to this problem, it is supposed to be an equation with two solutions? (x/3) = (4/x+1)Thank you

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Can you help me solve and show solution to this problem, it is supposed to be an equation with two solutions? (x/3) = (4/x+1)Thank you      Log On


   

Question 288761: Can you help me solve and show solution to this problem, it is supposed to be an equation with two solutions? (x/3) = (4/x+1)Thank you
Answer by texttutoring(324) About Me  (Show Source):
You can put this solution on YOUR website!
You need to cross-multiply:
x%2F3+=+4%2F%28x%2B1%29
x%28x%2B1%29=4%283%29
x%5E2%2Bx=12

Now set the right side to zero so that you can solve by factoring:

x%5E2%2Bx-12=0

Ask yourself, what two numbers multiply to -12, and when you add them up, they equal +1? The answer is +4 and -3:
%28x%2B4%29%28x-3%29=0

So you have two options:
either x+4=0, meaning x=-4
or x-3=0, meaning x=3

So your two solutions are x=-4, and x=3.