SOLUTION: solve the equation and indicate any extraneous solutions https://ibb.co/b3qHwa thanks for the help

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Question 1090044: solve the equation and indicate any extraneous solutions
https://ibb.co/b3qHwa
thanks for the help
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F%28x-3%29-%2822x%5E2-20x-9-4x%5E3%29%2F%282x%5E2-5x-3%29%2B2=2%2F%282x%2B1%29

x%2F%28x-3%29-%2822x%5E2-20x-9-4x%5E3%29%2F%282x%5E2-6x%2Bx-3%29%2B2=2%2F%282x%2B1%29









%282x%5E2+%2B+x-22x%5E2%2B20x%2B9%2B4x%5E3%2B4x%5E2-10x-6%29%2F%28x+-+3%29=2

4x%5E3+-+16x%5E2+%2B+11x+%2B+3=2%28x+-+3%29

4x%5E3+-+16x%5E2+%2B+11x+%2B+3=2x+-+6

4x%5E3+-+16x%5E2+%2B+11x+%2B+3-2x+%2B6=0

4x%5E3+-+16x%5E2+%2B+9x+%2B+9=0

%28x+-+3%29+%282+x+-+3%29+%282x+%2B+1%29+=+0
solutions:
x=3-> exclude this one because it will make denominator x%2Fhighlight%28%28x-3%29%29 equal to zero
x=3%2F2-> real solution
x=-1%2F2-> exclude this one because it will make denominator highlight%28%2822x%5E2-20x-9-4x%5E3%29%2F%282x+%2B+1%29%29 equal to zero