Chapter 7: Q. 97 (page 667)

In the following exercises, add or subtract.
$\frac{2 b^{2} + 30 b - 13}{b^{2} - 49} - \frac{2 b^{2} - 5 b - 8}{49 - b^{2}}$

Short Answer

Expert verified

The difference of the expressions is $\frac{4 b - 3}{b - 7}$ .

Step by step solution

Step 1. Given Information

The given expression is $\frac{2 b^{2} + 30 b - 13}{b^{2} - 49} - \frac{2 b^{2} - 5 b - 8}{49 - b^{2}}$ .

Step 2. Equalise the denominators

Multiply the numerator and denominator of the second term by $- 1$ to make both the numerators equal.

$\frac{2 b^{2} + 30 b - 13}{b^{2} - 49} - \frac{2 b^{2} - 5 b - 8}{49 - b^{2}} = \frac{2 b^{2} + 30 b - 13}{b^{2} - 49} - \frac{- 2 b^{2} + 5 b + 8}{b^{2} - 49}$

Step 3. Subtract the numerators

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

$\begin{array}{rcl} \frac{2 b^{2} + 30 b - 13}{b^{2} - 49} - \frac{- 2 b^{2} + 5 b + 8}{b^{2} - 49} & = & \frac{2 b^{2} + 30 b - 13 - (- 2 b^{2} + 5 b + 8)}{b^{2} - 49} \\ = & \frac{2 b^{2} + 30 b - 13 + 2 b^{2} - 5 b - 8}{b^{2} - 49} \\ = & \frac{4 b^{2} + 25 b - 21}{b^{2} - 49} \end{array}$

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.

$\begin{array}{rcl} \frac{4 b^{2} + 25 b - 21}{b^{2} - 49} & = & \frac{(4 b - 3) (b + 7)}{(b - 7) (b + 7)} \\ = & \frac{4 b - 3}{b - 7} \end{array}$

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In the following exercises, add or subtract.
$\frac{2 b^{2} + 30 b - 13}{b^{2} - 49} - \frac{2 b^{2} - 5 b - 8}{49 - b^{2}}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Equalise the denominators

Step 3. Subtract the numerators

Step 4. Factor the numerator and denominator

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In the following exercises, add or subtract.2b2+30b-13b2-49-2b2-5b-849-b2

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Equalise the denominators

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

Pure Maths

Statistics

Mechanics Maths

Decision Maths

Probability and Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, add or subtract.
$\frac{2 b^{2} + 30 b - 13}{b^{2} - 49} - \frac{2 b^{2} - 5 b - 8}{49 - b^{2}}$