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Essential Calculus: Early Transcendentals
Found in: Page 335
Essential Calculus: Early Transcendentals

Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280

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Short Answer

suppose that F,G and Q are polynomials and \(\frac{{F(x)}}{{Q(x)}} = \frac{{G(x)}}{{Q(x)}}\) for all x except when \(Q(x) = 0\).prove that \(F(x) = G(x)\) for all x.

we can prove that \(F(x) = G(x)\) for all x by using cross multiplication

See the step by step solution

Step by Step Solution

Step 1: Write the given data

Let us consider

\(\frac{{F(x)}}{{Q(x)}} = \frac{{G(x)}}{{Q(x)}}\)

We know that all the functions are polynomials.

By the definition we know that F,G, Q are all continuous

Step2: Apply the cross multiplication

So therefore we can cross multiply equations.

\(F(x)Q(x) = G(x)Q(x)\) and \(Q(x) \ne 0\)

Since all are continuous for all x, so we can divide by \(Q(x)\) to obtain

\(F(x) = G(x)\)

Hence, we can prove that \(F(x) = G(x)\) for all x.

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