Chapter 7: Q. 95 (page 667)

In the following exercises, add or subtract.
$\frac{z^{2} + 6 z}{z^{2} - 25} - \frac{3 z + 20}{25 - z^{2}}$

Short Answer

Expert verified

The required result is $\frac{z + 4}{z - 5}$ .

Step by step solution

Step 1. Given Information

The given expression is $\frac{z^{2} + 6 z}{z^{2} - 25} - \frac{3 z + 20}{25 - z^{2}}$ .

Step 2. Multiply the numerator and denominator of second expression by -1.

Multiply the numerator and denominator of the second term by $- 1$ .

$\frac{z^{2} + 6 z}{z^{2} - 25} - \frac{3 z + 20}{25 - z^{2}} = \frac{z^{2} + 6 z}{z^{2} - 25} - \frac{- 3 z - 20}{z^{2} - 25}$

Step 3. Subtract the numerators

As the denominators of the rational expressions is equal, subtract the numerators and place them over a common denominator.

$\begin{array}{rcl} \frac{z^{2} + 6 z}{z^{2} - 25} - \frac{- 3 z - 20}{z^{2} - 25} & = & \frac{z^{2} + 6 z - (- 3 x - 20)}{z^{2} - 25} \\ = & \frac{z^{2} + 6 z + 3 z + 20}{z^{2} - 25} \\ = & \frac{z^{2} + 9 z + 20}{z^{2} - 25} \end{array}$

Step 4. Factor the numerator and denominator

Factor the expression in the numerator and denominator and then cancel out the common terms in numerator and denominator.

$\begin{array}{rcl} \frac{z^{2} + 9 z + 20}{z^{2} - 25} & = & \frac{(z + 4) (z + 5)}{(z + 5) (z - 5)} \\ = & \frac{z + 4}{z - 5} \end{array}$

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In the following exercises, add or subtract.
$\frac{z^{2} + 6 z}{z^{2} - 25} - \frac{3 z + 20}{25 - z^{2}}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Multiply the numerator and denominator of second expression by -1.

Step 3. Subtract the numerators

Step 4. Factor the numerator and denominator

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In the following exercises, add or subtract. z2+6zz2-25-3z+2025-z2

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Multiply the numerator and denominator of second expression by -1.

Step 3. Subtract the numerators

Step 4. Factor the numerator and denominator

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Mechanics Maths

Geometry

Logic and Functions

Theoretical and Mathematical Physics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, add or subtract.
$\frac{z^{2} + 6 z}{z^{2} - 25} - \frac{3 z + 20}{25 - z^{2}}$