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Given the function h(x)= (x-2)/(3x+4) and g(x)= (x+5)/x, determine the point(s) of intersection.

 Feb 20, 2021

Best Answer 

 #1
avatar+944 
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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 \(-\frac{17}{4} \pm \frac{\sqrt{129}}{4}.\)

 Feb 20, 2021
 #1
avatar+944 
+1
Best Answer

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 \(-\frac{17}{4} \pm \frac{\sqrt{129}}{4}.\)

CubeyThePenguin Feb 20, 2021

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