Suggested languages for you:

Americas

Europe

Q45E

Expert-verifiedFound in: Page 335

Book edition
2nd

Author(s)
James Stewart

Pages
830 pages

ISBN
9781133112280

**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

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

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.

94% of StudySmarter users get better grades.

Sign up for free