Chapter 11: Q. 404 (page 1069)

In the following exercises, perform the indicated operations.
$\frac{5 t^{2} + 4 t + 3}{t^{2} - 25} - \frac{4 t^{2} - 8 t - 32}{t^{2} - 25}$

Short Answer

Expert verified

The expression is simplified as $\frac{t + 7}{t - 5}$

Step by step solution

Step 1. Given information

Expression:

$\frac{5 t^{2} + 4 t + 3}{t^{2} - 25} - \frac{4 t^{2} - 8 t - 32}{t^{2} - 25}$

here denominator in both fraction is same.

Step 2. Subtract the numerator of both fractions by keeping the denominator same.

$\frac{(5 t^{2} + 4 t + 3) - (4 t^{2} - 8 t - 32)}{t^{2} - 25} = \frac{5 t^{2} + 4 t + 3 - 4 t^{2} + 8 t + 32}{t^{2} - 25} = \frac{t^{2} + 12 t + 35}{t^{2} - 25}$

Step 3. Factorize numerator and denominator

$\frac{t^{2} + 7 t + 5 t + 35}{t^{2} - 5^{2}} = \frac{t (t + 7) + 5 (t + 7)}{(t - 5) (t + 5)} = \frac{(t + 5) (t + 7)}{(t - 5) (t + 5)}$

Step 4. Cancel common factor in numerator and denominator

$\frac{t + 7}{t - 5}$

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In the following exercises, perform the indicated operations.
$\frac{5 t^{2} + 4 t + 3}{t^{2} - 25} - \frac{4 t^{2} - 8 t - 32}{t^{2} - 25}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Subtract the numerator of both fractions by keeping the denominator same.

Step 3. Factorize numerator and denominator

Step 4. Cancel common factor in numerator and denominator

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In the following exercises, perform the indicated operations. 5t2+4t+3t2-25-4t2-8t-32t2-25

Short Answer

Step by step solution

Step 1. Given information

Step 2. Subtract the numerator of both fractions by keeping the denominator same.

Step 3. Factorize numerator and denominator

Step 4. Cancel common factor in numerator and denominator

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Calculus

Theoretical and Mathematical Physics

Probability and Statistics

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, perform the indicated operations.
$\frac{5 t^{2} + 4 t + 3}{t^{2} - 25} - \frac{4 t^{2} - 8 t - 32}{t^{2} - 25}$