Chapter 8: Q 247 (page 955)

Subtract $\frac{z + 2}{z - 5} - \frac{z}{z + 1}$ .

Short Answer

Expert verified

The result is $\frac{2 (4 z + 1)}{(z - 5) (z + 1)}$ .

Step by step solution

Given Information

The Given expression is $\frac{z + 2}{z - 5} - \frac{z}{z + 1}$ .

Find the LCD of denominators.

Since there are no common denominators.

The LCD is $(z - 5) (z + 1)$ .

Rewrite each fraction as an equivalent fraction with the LCD.

$= \frac{(z + 2) (z + 1)}{(z - 5) (z + 1)} - \frac{z (z - 5)}{(z - 5) (z + 1)}$

Simplify numerators.

$= \frac{z^{2} + 2 z + z + 2}{(z - 5) (z + 1)} - \frac{z^{2} - 5 z}{(z - 5) (z + 1)}$

$= \frac{z^{1} + 3 z + 2}{(z - 5) (z + 1)} - \frac{z^{2} - 5 z}{(z - 5) (z + 1)}$

Subtract and simplify the numerator.

Take common denominator.

$= \frac{z^{2} + 3 z + 2 - (z^{2} - 5 z)}{(z - 5) (z + 1)}$

$= \frac{z^{2} + 3 z + 2 - z^{2} + 5 z}{(z - 5) (z + 1)}$

Simplify.

$= \frac{8 z + 2}{(z - 5) (z + 1)}$

$= \frac{2 (4 z + 1)}{(z - 5) (z + 1)}$

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Subtract $\frac{z + 2}{z - 5} - \frac{z}{z + 1}$ .

Short Answer

Step by step solution

Given Information

Find the LCD of denominators.

Rewrite each fraction as an equivalent fraction with the LCD.

Subtract and simplify the numerator.

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Subtractz+2z-5-zz+1.

Short Answer

Step by step solution

Given Information

Find the LCD of denominators.

Rewrite each fraction as an equivalent fraction with the LCD.

Subtract and simplify the numerator.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Calculus

Discrete Mathematics

Geometry

Logic and Functions

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Subtract $\frac{z + 2}{z - 5} - \frac{z}{z + 1}$ .