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Solving Using Quadratic Formula When D>0

Solve the fol...

Question

Solve the following equation:

$\frac{2 x}{x - 3} + \frac{1}{2 x + 3} + \frac{3 x + 9}{(x - 3) (2 x + 3)} = 0; x \neq 3, x \neq - \frac{3}{2}$

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Solution

$fraction numerator 2 x over denominator x minus 3 end fraction plus fraction numerator 1 over denominator 2 x plus 3 end fraction plus fraction numerator 3 x plus 9 over denominator left parenthesis x minus 3 right parenthesis left parenthesis 2 x plus 3 right parenthesis end fraction equals 0 fraction numerator 2 x up diagonal strike left parenthesis x minus 3 right parenthesis end strike left parenthesis 2 x plus 3 right parenthesis over denominator up diagonal strike x minus 3 end strike end fraction plus fraction numerator left parenthesis x minus 3 right parenthesis up diagonal strike left parenthesis 2 x plus 3 right parenthesis end strike over denominator up diagonal strike left parenthesis 2 x plus 3 right parenthesis end strike end fraction plus fraction numerator up diagonal strike left parenthesis x minus 3 right parenthesis left parenthesis 2 x plus 3 right parenthesis end strike left parenthesis 3 x plus 9 right parenthesis over denominator up diagonal strike left parenthesis x minus 3 right parenthesis left parenthesis 2 x plus 3 right parenthesis end strike end fraction equals 0 2 x left parenthesis 2 x plus 3 right parenthesis plus left parenthesis x minus 3 right parenthesis plus left parenthesis 3 x plus 9 right parenthesis equals 0 4 x squared plus 6 x plus x minus 3 plus 3 x plus 9 equals 0 4 x squared plus 10 x plus 6 equals 0 h e r e comma space a equals 4 comma space b equals 10 comma space c equals 6 x equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction space space equals fraction numerator negative 10 plus-or-minus square root of 10 squared minus 4 cross times 4 cross times 6 end root over denominator 2 cross times 4 end fraction space space equals fraction numerator negative 10 plus-or-minus square root of 100 minus 96 end root over denominator 8 end fraction space space equals fraction numerator negative 10 plus-or-minus square root of 4 over denominator 8 end fraction space space equals fraction numerator negative 10 plus-or-minus 2 over denominator 8 end fraction x equals fraction numerator negative 10 plus 2 over denominator 8 end fraction space space space space space space space o r space space space x equals fraction numerator negative 10 minus 2 over denominator 8 end fraction bold space bold italic x bold space bold equals bold minus bold 1 space space space space space space space space space space space space space space space space space space o r space space space space x equals negative 3 over 2 space left parenthesis space n e g l e c t e d space a s space p e r space q u e s t i o n space left square bracket space x not equal to negative fraction numerator begin display style 3 end style over denominator begin display style 2 end style end fraction space right square bracket space right parenthesis space$

Hence, x = -1

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Similar questions

Q. Solve the given quadratic equation by factorization method

\frac{2 x}{x - 3} + \frac{1}{2 x + 3} + \frac{3 x + 9}{(x - 3) (2 x + 3)} = 0

\frac{2 x}{x - 3} + \frac{1}{2 x + 3} + \frac{3 x + 9}{(x - 3) (2 x + 3)} = 0

x + 1

Q. Solve the equations:

\frac{2 x^{3} - 3 x^{2} + x + 1}{2 x^{3} - 3 x^{2} - x - 1} = \frac{3 x^{3} - x^{2} + 5 x - 13}{3 x^{3} - x^{2} - 5 x + 13}

\frac{2 x - 1}{x + 3} + \frac{1 - 2 x}{x - 3} = \frac{4 - 3 x}{x^{2} - 9}

Q. Solve the following equation:

\frac{3 (x - 2) + 4 \sqrt{2 x^{3} - 3 x + 1}}{2 (x^{3} - 1)} = 1

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