Chapter 9: Q32. (page 476)

Simplify the expression $\frac{5 x^{2} + 10 x - 75}{4 x^{2} - 24 x - 28} \cdot \frac{2 x^{2} - 10 x - 28}{x^{2} + 7 x + 10}$

Short Answer

Expert verified

The simplified value of expression is $\frac{5 (x - 3)}{2 (x + 1)}$

Step by step solution

Step 1. Write down the given expression.

The given expression is $\frac{5 x^{2} + 10 x - 75}{4 x^{2} - 24 x - 28} \cdot \frac{2 x^{2} - 10 x - 28}{x^{2} + 7 x + 10}$

Step 2. Simplify the expression.

The given expression $\frac{5 x^{2} + 10 x - 75}{4 x^{2} - 24 x - 28} \cdot \frac{2 x^{2} - 10 x - 28}{x^{2} + 7 x + 10}$ is simplified as:

$\begin{matrix} \frac{5 x^{2} + 10 x - 75}{4 x^{2} - 24 x - 28} \cdot \frac{2 x^{2} - 10 x - 28}{x^{2} + 7 x + 10} = \frac{5 (x^{2} + 2 x - 15)}{4 (x^{2} - 6 x - 7)} \cdot \frac{2 (x^{2} - 5 x - 14)}{x^{2} + 7 x + 10} \\ = \frac{5 (x + 5) (x - 3)}{4 (x - 7) (x + 1)} \cdot \frac{2 (x - 7) (x + 2)}{(x + 5) (x + 2)} \\ = \frac{5}{2} \cdot \frac{(x - 7) (x + 2) (x + 5) (x - 3)}{(x + 5) (x + 2) (x - 7) (x + 1)} \\ = \frac{5 (x - 3)}{2 (x + 1)} \end{matrix}$

Step 3. Conclusion.

The simplified value of expression is $\frac{5 (x - 3)}{2 (x + 1)}$

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Simplify the expression $\frac{5 x^{2} + 10 x - 75}{4 x^{2} - 24 x - 28} \cdot \frac{2 x^{2} - 10 x - 28}{x^{2} + 7 x + 10}$

Short Answer

Step by step solution

Step 1. Write down the given expression.

Step 2. Simplify the expression.

Step 3. Conclusion.

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Simplify the expression5x2+10x−754x2−24x−28⋅2x2−10x−28x2+7x+10

Short Answer

Step by step solution

Step 1. Write down the given expression.

Step 2. Simplify the expression.

Step 3. Conclusion.

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Theoretical and Mathematical Physics

Geometry

Probability and Statistics

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

Simplify the expression $\frac{5 x^{2} + 10 x - 75}{4 x^{2} - 24 x - 28} \cdot \frac{2 x^{2} - 10 x - 28}{x^{2} + 7 x + 10}$