Question

Solve a / a-1 - a+5/a =0. Enter your solution as an improper fraction or as a decimal rounded to the nearest hundredth

Answer 1

Answer: $1\dfrac{1}{4}$

Step-by-step explanation:

Given

The equation in terms of a is

$\Rightarrow \dfrac{a}{a-1}-\dfrac{a+5}{a}=0\\\\\Rightarrow \dfrac{a}{a-1}=\dfrac{a+5}{a}\\\\\Rightarrow a^2=(a-1)(a+5)\\\\\Rightarrow a^2=a^2+4a-5\\\\ \Rightarrow 4a=5\\\\\Rightarrow a=\dfrac{5}{4}\ \text{or}\ 1\dfrac{1}{4}$