SOLUTION: Use the equation: ((1)/(2x+6)) + ((x)/(4))=((2x)/(x^2+3x+2)) a. Multiply each side by the LCD. Write the equation as a polynomial equation p(x)=0. b. Show that the polynomial p

Algebra ->  Rational-functions -> SOLUTION: Use the equation: ((1)/(2x+6)) + ((x)/(4))=((2x)/(x^2+3x+2)) a. Multiply each side by the LCD. Write the equation as a polynomial equation p(x)=0. b. Show that the polynomial p      Log On


   

Question 415798: Use the equation: ((1)/(2x+6)) + ((x)/(4))=((2x)/(x^2+3x+2))
a. Multiply each side by the LCD. Write the equation as a polynomial equation p(x)=0.
b. Show that the polynomial p(x) on the left side of the equation from part (a.) is the square of a trinomial of the form x^2+Bx+C.
c. What are the solutions to the equation.
I would really appreciate help on this, the whole question just confuses me. Thanks! :)
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Use the equation: ((1)/(2x+6)) + ((x)/(4))=((2x)/(x^2+3x+2))
Factor the denominators:
x/[2(x+3)] + x/4 = (2x)/[(x+2)(x+1)
LCD = 4x(x+1)(x+2)(x+3)
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a. Multiply each side by the LCD.
x[4(x+1)(x+2)(x+3)] + [x[x(x+1)(x+2)(x+3)] = (2x)[4x(x+3)]
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Write the equation as a polynomial equation p(x)=0.
x[4(x+1)(x+2)(x+3)] + [x[x(x+1)(x+2)(x+3)] - (2x)[4x(x+3)] = 0
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b. Show that the polynomial p(x) on the left side of the equation from part (a.) is the square of a trinomial of the form x^2+Bx+C.
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I'll leave that to you.
Square (x^2+Bx+C) and compare it to the left side term by term.
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Cheers,
Stan H.
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