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

bingboy Feb 20, 2024

+1633

+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

proyaop · Answer 1 · 2024-02-20T04:10:52

$\frac{a}{3} + 1 = \frac{a + 3}{a} + 1$

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: $a = {3 \pm\sqrt{9+36}\over2}={3\pm3\sqrt{5}\over2}$