+33 Given the function h(x)= (x-2)/(3x+4) and g(x)= (x+5)/x, determine the point(s) of intersection.
+1223 We are essentially finding the solutions to \(\frac{x-2}{3x+4} = \frac{x+5}{x}\).
Cross multiply: \((x-2)(x) =(3x+4)(x+5)\)
\(x^2-2x =3x^2 + 19x + 20\)
\(0 = 2x^2 + 21x + 20\)
Using the quadratic formula, we see that the solutions are at \(-\frac{17}{4} \pm \frac{\sqrt{129}}{4}.\)
+1223 We are essentially finding the solutions to \(\frac{x-2}{3x+4} = \frac{x+5}{x}\).
Cross multiply: \((x-2)(x) =(3x+4)(x+5)\)
\(x^2-2x =3x^2 + 19x + 20\)
\(0 = 2x^2 + 21x + 20\)
Using the quadratic formula, we see that the solutions are at \(-\frac{17}{4} \pm \frac{\sqrt{129}}{4}.\)
