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Find all values of a that satsify the equation \frac{a}{3} + 1 = \frac{a + 3}{a} + 1.

 Feb 20, 2024

Best Answer 

 #1
avatar+1622 
+1

\(\frac{a}{3} + 1 = \frac{a + 3}{a} + 1\)

Subtract 1 from both sides: \({a\over3}={a+3\over{a}}\)

Cross multiply: \(a^2=3a+9\)\(a^2-3a-9=0\)

Use quadratic formula: \(a = {3 \pm\sqrt{9+36}\over2}={3\pm3\sqrt{5}\over2}\)

 Feb 20, 2024
 #1
avatar+1622 
+1
Best Answer

\(\frac{a}{3} + 1 = \frac{a + 3}{a} + 1\)

Subtract 1 from both sides: \({a\over3}={a+3\over{a}}\)

Cross multiply: \(a^2=3a+9\)\(a^2-3a-9=0\)

Use quadratic formula: \(a = {3 \pm\sqrt{9+36}\over2}={3\pm3\sqrt{5}\over2}\)

proyaop Feb 20, 2024

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