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

fortdefruitI 2021-09-29 Answered
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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Expert Answer

Corben Pittman
Answered 2021-09-30 Author has 11953 answers
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 \(\displaystyle{\frac{{{x}-{a}}}{{{x}-{b}}}}={\frac{{{a}}}{{{b}}}}\).
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