Chapter 11: Q12. (page 699)

Simplify the given expression. State the excluded values of the variables.
$\frac{z - 5}{z^{2} - 7 z + 10}$

Short Answer

Expert verified

The simplified expression is $\frac{1}{z - 2}$ .

The excluded values are $z = 2, 5$ .

Step by step solution

Step 1. Define a rational function.

A function of the form $y = \frac{p}{q}$ is called a rational function, where $p$ and $q$ are the polynomials and $q \neq 0$ .

Step 2. Define the excluded values for the rational function.

Any value of a variable that results in a denominator of zero in a rational function is excluded from the domain of the function and these values are called the excluded values of the rational function.

Step 3. Simplify the expression z−5z2−7z+10.

Factor the denominator to simplify the expression $\frac{z - 5}{z^{2} - 7 z + 10}$ .

$\begin{array}{l} \frac{z - 5}{z^{2} - 7 z + 10} = \frac{z - 5}{z^{2} - 5 z - 2 z + 10} \\ = \frac{z - 5}{z (z - 5) - 2 (z - 5)} \\ = \frac{z - 5}{(z - 5) (z - 2)} \\ = \frac{1}{z - 2} \end{array}$

Step 4. State the excluded values of the variable for the expression z−5z2−7z+10.

For excluded value,

Denominator $= 0$

$\begin{array}{l} z^{2} - 7 z + 10 = 0 \\ z^{2} - 5 z - 2 z + 10 = 0 \\ z (z - 5) - 2 (z - 5) = 0 \\ (z - 5) (z - 2) = 0 \\ z = 2, 5 \end{array}$

Therefore,

The simplified expression is $\frac{1}{z - 2}$ .

The excluded values are $z = 2, 5$ .

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Simplify the given expression. State the excluded values of the variables.
$\frac{z - 5}{z^{2} - 7 z + 10}$

Short Answer

Step by step solution

Step 1. Define a rational function.

Step 2. Define the excluded values for the rational function.

Step 3. Simplify the expression z−5z2−7z+10.

Step 4. State the excluded values of the variable for the expression z−5z2−7z+10.

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Simplify the given expression. State the excluded values of the variables.z−5z2−7z+10

Short Answer

Step by step solution

Step 1. Define a rational function.

Step 2. Define the excluded values for the rational function.

Step 3. Simplify the expression z−5z2−7z+10.

Step 4. State the excluded values of the variable for the expression z−5z2−7z+10.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Probability and Statistics

Statistics

Mechanics Maths

Pure Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Simplify the given expression. State the excluded values of the variables.
$\frac{z - 5}{z^{2} - 7 z + 10}$