Question

Which of the following is not an extraneous root for in the following equation:
$5(\frac{x}{x+1}{)}^2-4(\frac{x}{x+1})-1=0$

• A. -1/5
• B. -1/8
• C. -1/6
• D. -1/10

Answer 1

The correct option is C -1/6

We have
$5(\frac{x}{x+1}{)}^2-4(\frac{x}{x+1})-1=0$
Let $\frac{x}{x+1}=m$, then we have,
$5m^2-4m-1=0$
$\Rightarrow 5m^2-5m+m-1=0$
$\Rightarrow 5m(m-1)+(m-1)=0$
$\Rightarrow (5m+1)(m-1)=0$
$\Rightarrow m=-\frac{1}{5}$ or $m=1$
$Form=-\frac{1}{5}$
$\frac{x}{x+1}=-\frac{1}{5}\Rightarrow 5x=-x-1\Rightarrow x=-\frac{1}{6}$
$Form=1$
$\frac{x}{x+1}=1\Rightarrow x=x+1$
So, no value of x at m = 1.
Extraneous root is a root which doesn't satisfy the given equation.
Hence, correct option is c.