SOLUTION: can someone please help me solve the following equations for x 1) 6/x+3=9x/x^2-9 2) sqrt2x+3=5 3) x^3-2x^2-x=2 given x=1 is one solution. Thank you

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: can someone please help me solve the following equations for x 1) 6/x+3=9x/x^2-9 2) sqrt2x+3=5 3) x^3-2x^2-x=2 given x=1 is one solution. Thank you       Log On


   

Question 483274: can someone please help me solve the following equations for x
1) 6/x+3=9x/x^2-9
2) sqrt2x+3=5
3) x^3-2x^2-x=2 given x=1 is one solution.
Thank you
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
1) We write the equation in the simple way to find the LCD:
6%2F%28x%2B3%29=9x%2F%28x%2B3%29%28x-3%29.Assuming x different from 3 and -3, multiply both
sides by (x+3)(x-3) and get:6%28x-3%29=9x<=>3x=-18<=>x=-6.
2)sqrt%282x%2B3%29=5 Squaring both sides we get:2x+3=25<=>2x=22<=>x=11.
3)Since x=1 is a solution the polynomial x%5E3-2x%5E2-x-2 is divisible by x-1
%28x%5E3-2x%5E2-x-2%29%2F%28x-1%29=x%5E2-x-2<=>x%5E3-2x%5E2-x-2=%28x-1%29%28x%5E2-x-2%29
To find the other roots we solve the quadratic equation:
x%5E2-x-2=0<=>%28x-2%29%28x%2B1%29=0. The solution set for the original equation
is:{-1, 1, 2}.