Chapter 5: Q. 7 (page 441)

Show that the equation $p (x) = q (x) m (x) + R (x)$ is equivalent to the equation $\frac{p (x)}{q (x)} = m (x) + \frac{R (x)}{q (x)}$ for all x for which q(x) is nonzero.

Short Answer

Expert verified

The given equation has been proved.

Step by step solution

Step 1. Given Information

The given equation is $p (x) = q (x) m (x) + R (x)$

Step 2. Proof

Divide both the sides of the given equation by q(x) after that simplify the equation.

$\frac{p (x)}{q (x)} = \frac{q (x) m (x) + R (x)}{q (x)} \frac{p (x)}{q (x)} = \frac{q (x) m (x)}{q (x)} + \frac{R (x)}{q (x)} \frac{p (x)}{q (x)} = m (x) + \frac{R (x)}{q (x)}$

Thus, the equation is proved.

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Show that the equation $p (x) = q (x) m (x) + R (x)$ is equivalent to the equation $\frac{p (x)}{q (x)} = m (x) + \frac{R (x)}{q (x)}$ for all x for which q(x) is nonzero.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Proof

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Show that the equation p(x)=q(x)m(x)+R(x)is equivalent to the equation p(x)q(x)=m(x)+R(x)q(x)for all x for which q(x) is nonzero.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Proof

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Applied Mathematics

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Show that the equation $p (x) = q (x) m (x) + R (x)$ is equivalent to the equation $\frac{p (x)}{q (x)} = m (x) + \frac{R (x)}{q (x)}$ for all x for which q(x) is nonzero.