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 ...
[tex]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\}[/tex]
Solutions rounded to hundredths are ...
x = -0.44
x = 1.69
_____
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
