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Found in: Page 335

### Essential Calculus: Early Transcendentals

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

See the 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.