# Determine whether the given value is a solution of the equation.

Determine whether the given value is a solution of the equation.
$$\displaystyle{\frac{{{x}-{a}}}{{{x}-{b}}}}={\frac{{{a}}}{{{b}}}}{\left({b}\ne{0}\right)}$$
(a)x=0
(b)x=b

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Corben Pittman
Step 1
The given equation is $$\displaystyle{\frac{{{x}-{a}}}{{{x}-{b}}}}={\frac{{{a}}}{{{b}}}}$$
Step 2
Substitute x=0 in given equation,
$$\displaystyle{L}.{H}.{S}={\frac{{{x}-{a}}}{{{x}-{b}}}}$$
$$\displaystyle={\frac{{{0}-{a}}}{{{0}-{b}}}}$$
$$\displaystyle={\frac{{-{a}}}{{-{b}}}}$$
$$\displaystyle={\frac{{{a}}}{{{b}}}}$$
=R.H.S
So, the given value x=0 is a solution of the equation $$\displaystyle{\frac{{{x}-{a}}}{{{x}-{b}}}}={\frac{{{a}}}{{{b}}}}$$.
Step 3
Substitute x=b in given equation,
$$\displaystyle{L}.{H}.{S}={\frac{{{x}-{a}}}{{{b}-{b}}}}$$
$$\displaystyle={\frac{{{x}-{a}}}{{{0}}}}$$
we cannot divide by zero, so it is undefined.
So, the given value x=b is not a solution of the equation $$\displaystyle{\frac{{{x}-{a}}}{{{x}-{b}}}}={\frac{{{a}}}{{{b}}}}$$.