Question

PLZ HELP ITS DUE TODAY

Answer 1

9514 1404 393

Answer:

  x = {-0.44, 1.69}

Step-by-step explanation:

Multiply by the denominator to eliminate the fraction.

  3 = x(4x -5)

  4x^2 -5x -3 = 0 . . . . . subtract 3 and put in standard form

Using the quadratic formula with a=4, b=-5, c=-3, we have the solutions as ...

  $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-5)\pm\sqrt{(-5)^2-4(4)(-3)}}{2(4)}\\\\x=\dfrac{5\pm\sqrt{73}}{8}\approx \{-0.443, 1.693\}$

Solutions rounded to hundredths are ...

  x = -0.44

  x = 1.69

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A graphing calculator can show the x-intercepts easily, so it works well to write the equation in the form

  f(x) = 0

  3/(4x -5) -x = 0