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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.

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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

#1
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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
+944
+1

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