SOLUTION: Solve the equation and check the solution. (Enter your answers as a comma-separated list. Simplify your answers completely. If there is no solution, enter NO SOLUTION.) Solve for b

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve the equation and check the solution. (Enter your answers as a comma-separated list. Simplify your answers completely. If there is no solution, enter NO SOLUTION.) Solve for b      Log On


   

Question 1130254: Solve the equation and check the solution. (Enter your answers as a comma-separated list. Simplify your answers completely. If there is no solution, enter NO SOLUTION.) Solve for b.
1 - 2/b = -3b/(b^2+2b)
Identify any extraneous values. (Enter your answers as a comma-separated list. Simplify your answers completely. If there are no extraneous values, enter NO SOLUTION.)
Found 3 solutions by Alan3354, josgarithmetic, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
What else would we do if there is no solution?

Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
If you will identify lowest or simplest denominator, b(b+2), and multiply the left and right sides by this b(b+2), and simplify, you should obtain
b%5E2%2B3b-4=0.

%28b%2B4%29%28b-1%29=0

One or both solutions are b=-4 or b=1.
Check each to see if either or both will work in original equation.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
1+-+2%2Fb+=+-3b%2F%28b%5E2%2B2b%29+
b%2Fb+-+2%2Fb+=+-3cross%28b%29%2Fcross%28b%29%28b%2B2%29+
%28b+-+2%29%2Fb+=+-3%2F%28b%2B2%29+.........cross multiply
%28b+-+2%29%28b%2B2%29++=+-3b
b%5E2+-+2%5E2+=+-3b
b%5E2+%2B3b-+4=+0
b%5E2+-b%2B4b-+4=+0
%28b%5E2+-b%29%2B%284b-+4%29=+0
b%28b+-1%29%2B4%28b-+1%29=+0
%28b%2B4%29%28b-+1%29=+0
solutions:
%28b%2B4%29=+0->b=-4
%28b-+1%29=+0->b=1

check the solutions:
1+-+2%2Fb+=+-3b%2F%28b%5E2%2B2b%29+->b=-4
1+-+2%2F-4+=+-%283%28-4%29%29%2F%28%28-4%29%5E2%2B2%28-4%29%29+
1+%2B+1%2F2+=+12%2F%2816-8%29+
2%2F2%2B1%2F2+=+12%2F8+
3%2F2+=+3%2F2+-> true; b=-4 is a solution

1+-+2%2Fb+=+-3b%2F%28b%5E2%2B2b%29+->b=1
1+-+2%2F1+=+-%283%281%29%29%2F%28%281%29%5E2%2B2%281%29%29+
1+-2+=+-3%2F%281%2B2%29+
-1=+-3%2F3+
-1+=+-1+-> true; b=1 is a solution

our answers:-4, 1

+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+1-+2%2Fx+%2C+-3x%2F%28x%5E2%2B2x%29%29+