Question

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 $x$. [Hint: Use continuity.]

          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 $x$. [Hint: Use continuity.]

Added by Darius C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

05/30/2023

Step 1

Now, let's consider the polynomial $H(x) = F(x)Q(x) - G(x)Q(x)$. We have $H(x) = 0$ for all $x$ except when $Q(x) = 0$. Now, we know that polynomials are continuous functions. Show more…

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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 $x$. [Hint: Use continuity.]