Question

Determine whether the given values are the solutions of the given equation or not. $\frac{x}{a}+\frac{b}{x}=\frac{a+b}{a};(x\ne 0),x=a,x=b.$

• A. Only $x=a$ is the solution of the equation
• B. Only $x=b$ is the solution of the equation
• C. Both $x=a,b$ are the solutions of the equation
• D. None of these

Answer 1

Answer: (C)

Both $x=a,b$ are the solutions of the equation

Simplifying, we get
$\frac{x}{a}+\frac{b}{x}=1+\frac{b}{a}$
Substituting $x=a$, we get
$1+\frac{b}{a}=1+\frac{b}{a}$
Hence $LHS=RHS$
Substituting $x=b$
we get
$\frac{b}{a}+1=1+\frac{b}{a}$
Hence $LHS=RHS$
Thus both are solutions to the given equation.