Chapter 7: Q. 93 (page 667)

In the following exercises, add or subtract.
$\frac{10 x^{2} + 16 x - 7}{8 x - 3} + \frac{2 x^{2} + 3 x - 1}{3 - 8 x}$

Short Answer

Expert verified

The sum of the expressions is $x + 2$ .

Step by step solution

Step 1. Given Information

The given expression is $\frac{10 x^{2} + 16 x - 7}{8 x - 3} + \frac{2 x^{2} + 3 x - 1}{3 - 8 x}$ .

Step 2. Multiply Numerator and denominator of the second fraction by -1

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

$\frac{10 x^{2} + 16 x - 7}{8 x - 3} + \frac{2 x^{2} + 3 x - 1}{3 - 8 x} = \frac{10 x^{2} + 16 x - 7}{8 x - 3} + \frac{- 2 x^{2} - 3 x + 1}{8 x - 3}$

Step 3. Add the Numerator

As the denominator is same for both the terms, add the numerator and place over the common denominator.
Add the like terms of the numerator.

$\begin{array}{rcl} \frac{10 x^{2} + 16 x - 7}{8 x - 3} + \frac{- 2 x^{2} - 3 x + 1}{8 x - 3} & = & \frac{10 x^{2} + 16 x - 7 - 2 x^{2} - 3 x + 1}{8 x - 3} \\ = & \frac{8 x^{2} + 13 x - 6}{8 x - 3} \end{array}$

Step 4. Simplify

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

$\begin{array}{rcl} \frac{8 x^{2} + 13 x - 6}{8 x - 3} & = & \frac{(8 x - 3) (x + 2)}{8 x - 3} \\ = & x + 2 \end{array}$

So, the sum is $x + 2$ .

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In the following exercises, add or subtract.
$\frac{10 x^{2} + 16 x - 7}{8 x - 3} + \frac{2 x^{2} + 3 x - 1}{3 - 8 x}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Multiply Numerator and denominator of the second fraction by -1

Step 3. Add the Numerator

Step 4. Simplify

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In the following exercises, add or subtract.10x2+16x-78x-3+2x2+3x-13-8x

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Multiply Numerator and denominator of the second fraction by -1

Step 3. Add the Numerator

Step 4. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Mechanics Maths

Decision Maths

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, add or subtract.
$\frac{10 x^{2} + 16 x - 7}{8 x - 3} + \frac{2 x^{2} + 3 x - 1}{3 - 8 x}$